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BEGIN:VEVENT
SUMMARY:Andrew Sageman-Furnas (University Göttingen)
DTSTART:20200421T170000Z
DTEND:20200421T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/1
DESCRIPTION:Title: Navigating the space of Chebyshev nets\nby Andrew Sageman-Furnas (
University Göttingen) as part of Online Seminar "Geometric Analysis"\n\n\
nAbstract\nMany materials are built from a grid of flexible but nearly ine
xtensible rods that behaves as a shell-like structure. Everyday examples r
ange from fabrics made of 1000s of interwoven yarns\; to kitchen strainers
made of 100s of plastically deforming wires\; to architectural gridshells
or medical stents made of 10s of elastically deforming rods. In this talk
\, I emphasize the geometric constraints common to these different physica
l systems. We build from a differential geometric model for woven fabric\,
initially introduced by Pafnuty Chebyshev in 1878\, that directly encodes
the inextensibility of the two families of rods.\n\nWe discuss the theory
of Chebyshev nets through a series of applied\, collaborative efforts in
computational fabrication and inverse design. Theoretical obstructions exp
ose the challenges in finding Chebyshev nets on surfaces with large amount
s of curvature\, suggesting a limited shape space. However\, we show that
a careful reformulation of the problem\, combined with a discrete analog o
f Chebyshev nets\, leads to computational tools that reveal a vibrant desi
gn space.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siran Li (Rice University)
DTSTART:20200421T180000Z
DTEND:20200421T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/2
DESCRIPTION:Title: Isometric Immersions of Riemannian Manifolds into Euclidean Spaces\, R
evisited\nby Siran Li (Rice University) as part of Online Seminar "Geo
metric Analysis"\n\n\nAbstract\nThe existence of isometric immersions of R
iemannian\nmanifolds into ambient Euclidean spaces has been a classical pr
oblem\nin geometric analysis and nonlinear PDEs. Seminal works by Darboux\
,\nWeyl\, Nirenberg\, Nash\, Gromov\, etc. etc. have addressed this proble
m\nfrom different perspectives. In this talk we discuss three approaches\,
\nsome are probably less known\, to the isometric immersions problem.\nThe
se include (1)\, pseudo-holomorphic curve formulation of the Weyl\nproblem
due to F. Labourie\; (2)\, Uhlenbeck gauge formulation for the\nPfaff sys
tem\; and (3)\, the fluid mechanical formulation for negatively\ncurved su
rfaces.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bastian Käfer (RWTH Aachen)
DTSTART:20200428T170000Z
DTEND:20200428T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/3
DESCRIPTION:Title: A Möbius invariant energy for sets of arbitrary dimension and codimen
sion\nby Bastian Käfer (RWTH Aachen) as part of Online Seminar "Geome
tric Analysis"\n\n\nAbstract\nWe consider the family of Möbius invariant
energies for m-dimensional submanifolds of $\\mathbb R^n$\, introduced by
R. Kusner and J. Sullivan\, defined on a class of sets\, which are given b
y the union of Lipschitz graphs and satisfy an additional condition of "ni
ce" self-intersection.\nWe show for these sets that finite energy implies
Reifenberg-flatness through estimating the energy of certain subsets.\nThi
s finally leads to a local representation given by a single graph and prev
ents any kind of self-intersection.\nAs an immediate implication\, we obta
in that every immersed $C^1$ manifold with finite energy is embedded.\nThi
s is joint work with Heiko von der Mosel.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huy The Nguyen (Queen Mary University London)
DTSTART:20200505T170000Z
DTEND:20200505T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/4
DESCRIPTION:Title: High codimension mean curvature flow and surgery\nby Huy The Nguye
n (Queen Mary University London) as part of Online Seminar "Geometric Anal
ysis"\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Ratzkin (University Würzburg)
DTSTART:20200512T170000Z
DTEND:20200512T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/5
DESCRIPTION:Title: On constant Q-curvature metrics with isolated singularities and a rela
ted fourth order conformal invariant\nby Jesse Ratzkin (University Wü
rzburg) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nThe
Q-curvature of a Riemannian manifold is a higher order analog of its scala
r curvature\, and so many people have over the last two decades proven res
ults about Q-curvature mirroring theorems about scalar curvature. I will p
resent two such results. First\, I will describe a refined asymptotic expa
nsion of isolated singularities in the conformally flat case\, similar to
work of Caffarelli\, Gidas and Spruck in the scalar curvature setting. The
n I will describe a conformal invariant and prove a convergence result sim
ilar to a theorem of Schoen.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volker Branding (University Vienna)
DTSTART:20200519T170000Z
DTEND:20200519T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/6
DESCRIPTION:Title: Higher order generalizations of harmonic maps\nby Volker Branding
(University Vienna) as part of Online Seminar "Geometric Analysis"\n\nAbst
ract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katharina Brazda (University Vienna)
DTSTART:20200526T170000Z
DTEND:20200526T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/7
DESCRIPTION:Title: The Canham-Helfrich model for multiphase biomembranes\nby Katharin
a Brazda (University Vienna) as part of Online Seminar "Geometric Analysis
"\n\n\nAbstract\nBiological membranes adopt a fascinating variety of shape
s. The Canham-Helfrich variational model describes their equilibrium confi
gurations as surfaces of minimal elastic bending energy under area and vol
ume constraints. In case of heterogeneous membranes with multiple phases\,
lateral fluidity gives rise to an additional coupling between composition
and curvature. We present an existence result for multiphase Canham-Helfr
ich minimizers with sharp phase interfaces obtained in the framework of or
iented curvature varifolds with boundary. This is joint work with Luca Lus
sardi and Ulisse Stefanelli.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miles Simon (University Magdeburg)
DTSTART:20200623T170000Z
DTEND:20200623T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/8
DESCRIPTION:Title: On the regularity of Ricci flows coming out of metric spaces.\nby
Miles Simon (University Magdeburg) as part of Online Seminar "Geometric An
alysis"\n\n\nAbstract\nJoint work with Alix Deruelle\, Felix Schulze\n\nWe
consider solutions to Ricci flow defined on manifolds M for a time interv
al $(0\,T)$ whose Ricci curvature is bounded uniformly in time from below\
, and for which the norm of the full curvature tensor at time $t$ is bou
nded by $c/t$ for some fixed constant $c>1$ for all $t \\in (0\,T)$.\nFrom
previous works\, it is known that if the solution is complete for all tim
es $t>0$\, then there is a limit\nmetric space $(M\,d_0)$\, as time t appr
oaches zero. We show : if there is a open region $V$ on which $(V\,d_0)$ i
s *smooth*\, then the\nsolution can be extended smoothly to time zero on $
V$.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Mäder-Baumdicker (University Darmstadt)
DTSTART:20200505T180000Z
DTEND:20200505T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/9
DESCRIPTION:Title: The Morse index of Willmore spheres and its relation to the geometry o
f minimal surfaces\nby Elena Mäder-Baumdicker (University Darmstadt)
as part of Online Seminar "Geometric Analysis"\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Remy Rodiac (University Paris-Saclay)
DTSTART:20200407T170000Z
DTEND:20200407T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/11
DESCRIPTION:Title: Inner variations and limiting vorticities for the Ginzburg-Landau equ
ations\nby Remy Rodiac (University Paris-Saclay) as part of Online Sem
inar "Geometric Analysis"\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Steenebrügge (RWTH Aachen)
DTSTART:20200414T170000Z
DTEND:20200414T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/12
DESCRIPTION:Title: A speed preserving Hilbert gradient flow for generalized integral Men
ger curvature\nby Daniel Steenebrügge (RWTH Aachen) as part of Online
Seminar "Geometric Analysis"\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Pegon (Université de Paris)
DTSTART:20200616T170000Z
DTEND:20200616T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/13
DESCRIPTION:Title: Partial regularity for fractional harmonic maps into spheres\nby
Marc Pegon (Université de Paris) as part of Online Seminar "Geometric Ana
lysis"\n\n\nAbstract\nSimilarly to “classical” harmonic maps\, which a
re critical points of the Dirichlet energy\, fractional harmonic maps are
defined as critical points of a fractional Dirichlet energy associated wit
h the $s$-power of the Laplacian\, for $s \\in (0\,1)$.\nIn this talk\, af
ter a brief reminder on classical harmonic maps\, I will present the fract
ional setting and the partial regularity results we have obtained for maps
valued into a sphere. In the case of half harmonic maps ($s=\\frac{1}{2}$
)\, I will also recall the connection with minimal surfaces with free boun
dary\, which allowed us to improve known regularity results for energy min
imizing maps into spheres.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Topping (University of Warwick)
DTSTART:20200630T170000Z
DTEND:20200630T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/14
DESCRIPTION:Title: Uniqueness of limits in geometric flows\nby Peter Topping (Univer
sity of Warwick) as part of Online Seminar "Geometric Analysis"\n\n\nAbstr
act\nQuite often when considering long-time behaviour of geometric flows\,
or considering blow-ups of singularities in geometric PDE\, we extract li
mits using soft compactness arguments. For example\, a flow might easily b
e seen to converge to a limit at a *sequence* of times converging to infin
ity.\nThe more subtle question is then whether the flow converges as time
converges to infinity\, without having to restrict to a sequence of times.
\n\nI will outline some of the issues that arise in this subject\, focussi
ng on gradient flows for the harmonic map energy\, and sketch some recent
work with M.Rupflin and J.Kohout.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruben Jakob (Technion)
DTSTART:20200707T170000Z
DTEND:20200707T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/15
DESCRIPTION:Title: Generic full smooth convergence of the elastic energy flow in the 2-s
phere\nby Ruben Jakob (Technion) as part of Online Seminar "Geometric
Analysis"\n\n\nAbstract\nThe speaker is going to present his recent invest
igation of the ``Moebius\ninvariant Willmore flow'' (MIWF) in the 3-sphere
and of some particular version of the\n``elastic energy flow'' (EEF) in t
he 2-sphere. We will discuss the\ninteraction between these two geometric
flows via the Hopf fibration and the\nresulting possibility to transfer pa
rticular insights about the ``EEF'' to\nthe ``MIWF''\, and vice versa spec
ial insights about the ``MIWF'' back\nto the ``EEF''. A big motivation for
this parallel investigation is the\nannounced proof (by the speaker) of t
he ''generic full smooth convergence''\nof the ``EEF'' in the 2-sphere.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Myfanwy Evans (University of Potsdam)
DTSTART:20200616T180000Z
DTEND:20200616T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/16
DESCRIPTION:Title: Geometric modelling of tangled structures\nby Myfanwy Evans (Univ
ersity of Potsdam) as part of Online Seminar "Geometric Analysis"\n\n\nAbs
tract\nThis talk will introduce the use of geometric ideas in the characte
risation and analysis of tangled biophysical systems. It will introduce th
e construction of idealised tangled structures using ideas of both symmetr
y and homotopy of tangled lines on surfaces. These structures provide an e
xtensive set of tangling motifs for the exploration of the behaviour of ta
ngled microstructures in liquids\, and I will show preliminary results wor
king towards this goal\, including an example of the geometry-driven swell
ing of human skin cells.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lynn Heller (University of Hannover)
DTSTART:20200602T170000Z
DTEND:20200602T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/17
DESCRIPTION:Title: Area Estimates for High genus Lawson surfaces via DPW\nby Lynn He
ller (University of Hannover) as part of Online Seminar "Geometric Analysi
s"\n\n\nAbstract\nStarting at a saddle tower surface\, we give a new exist
ence proof of the Lawson surfaces\n$\\xi_{m\,k}$ of high genus by dropping
some closing conditions of the surface and then\ndeforming the correspond
ing DPW potential. As a byproduct\, we obtain for fixed mestimates\non the
area of $\\xi_{m\,k}$ in terms of their genus $g= mk \\gg 1$. This is joi
nt work with\nSebastian Heller and Martin Traizet.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Pistre (RWTH Aachen University)
DTSTART:20200609T170000Z
DTEND:20200609T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/18
DESCRIPTION:Title: The Radon transform and higher regularity of surfaces minimising a Fi
nsler area\nby Sven Pistre (RWTH Aachen University) as part of Online
Seminar "Geometric Analysis"\n\n\nAbstract\nA Finsler metric is a smooth f
amily of smooth norms on the tangent bundle of a manifold. One possible ge
neralisation of the usual Riemannian notion of area in Finsler geometry is
the Busemann-Hausdorff area functional. In this talk I will consider high
-codimensional disk-type surfaces which minimise this area with respect to
Plateau boundary conditions. $\\\\$\nI will show that the Busemann-Hausdo
rff area functional fits into the Hildebrandt-von der Mosel framework on C
artan functionals. Existence of minimisers is then guaranteed under mild g
rowth conditions of the Finsler metric. Higher regularity ($W^{2\,2}_{\\te
xtrm{loc}} \\cap C^{1\,\\mu}$) of minimisers can be achieved by using func
tional analytic properties of the Radon transform. \n$\\\\$\nThe latter is
an operator which assigns a function on the $(n−1)$-sphere its mean by
integration over $(m-1)$-dimensional subspheres. One crucial property of t
his operator is its equivariance with respect to a Lie group action on the
sphere and the $m$-Grassmannian. An infinitesimal version of this equivar
iance yields the regularity results about area minimisers.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Bär (University of Potsdam)
DTSTART:20200714T170000Z
DTEND:20200714T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/19
DESCRIPTION:Title: Counter-intuitive approximations\nby Christian Bär (University o
f Potsdam) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nT
he Nash-Kuiper embedding theorem is a prototypical example of a counter-in
tuitive approximation result: any short embedding of a Riemannian manifold
into Euclidean space can be approximated by *isometric* ones. As a conseq
uence\, any surface can be isometrically $C^1$-embedded into an arbitraril
y small ball in $\\mathbb{R}^3$. For $C^2$-embeddings this is impossible d
ue to curvature restrictions.\n\nWe will present a general result which wi
ll allow for approximations by functions satisfying strongly overdetermine
d equations on open dense subsets. This will be illustrated by three examp
les: real functions\, embeddings of surfaces\, and abstract Riemannian met
rics on manifolds.\n\nOur method is based on "weak flexibility"\, a concep
t introduced by Gromov in 1986. This is joint work with Bernhard Hanke (Au
gsburg).\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carla Cederbaum (University of Tübingen)
DTSTART:20200721T170000Z
DTEND:20200721T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/20
DESCRIPTION:Title: On CMC-foliations of asymptotically flat manifolds\nby Carla Cede
rbaum (University of Tübingen) as part of Online Seminar "Geometric Analy
sis"\n\n\nAbstract\nIn 1996\, Huisken and Yau proved existence of foliatio
ns by constant mean curvature (CMC) surfaces in the asymptotic end of an a
symptotically Euclidean Riemannian manifold. Their work has inspired the s
tudy of various other foliations in asymptotic ends\, most notably the fol
iations by Willmore surfaces (Lamm\, Metzger\, Schulze) and by constant ex
pansion/null mean curvature surfaces in the context of asymptotically Eucl
idean initial data sets in General Relativity (Metzger). I will present a
new foliation by constant spacetime mean curvature surfaces (STCMC)\, also
in the context of asymptotically Euclidean initial data sets in General R
elativity (joint work with Sakovich). The STCMC-foliation is well-suited t
o define a notion of total center of mass in General Relativity.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadine Große
DTSTART:20200728T170000Z
DTEND:20200728T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/21
DESCRIPTION:Title: Boundary value problems on singular domains: an approach via bounded
geometries\nby Nadine Große as part of Online Seminar "Geometric Anal
ysis"\n\n\nAbstract\nIn this talk\, we consider boundary value problems on
domains \nwith non smooth boundaries. We approach this problem by transfe
rring it\nto non-compact manifolds with a suffiently nice geometry -- the
bounded geometry.\nThis gives a more general framework that allows to hand
le Dirichlet (or\nDirichlet-Neumann mixed) boundary value problems for dom
ains with a\nlarger class of singularities on the boundary and gives a nic
e geometric\ninterpretation. This is joint work with Bernd Ammann\n(Regens
burg) and Victor Nistor (Metz).\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melanie Rupflin (University of Oxford)
DTSTART:20200804T170000Z
DTEND:20200804T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/22
DESCRIPTION:Title: Łojasiewicz inequalities near simple bubble trees for the $H$ surfac
e equation\nby Melanie Rupflin (University of Oxford) as part of Onlin
e Seminar "Geometric Analysis"\n\n\nAbstract\nIn this talk we discuss a ga
p phenomenon for critical points of\nthe $H$-functional on closed non-sphe
rical surfaces when $H$ is constant\, and in\nthis setting furthermore pro
ve that sequences of almost critical points\nsatisfy Łojasiewicz inequali
ties as they approach the first non-trivial\nbubble tree.\n\nTo prove thes
e results we derive sufficient conditions for Łojasiewicz\ninequalities t
o hold near a finite-dimensional submanifold of\nalmost-critical points fo
r suitable functionals on a Hilbert space.\n\nThe presented results are jo
int work with Andrea Malchiodi and Ben Sharp.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Scheuer (Cardiff University)
DTSTART:20200811T170000Z
DTEND:20200811T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/23
DESCRIPTION:Title: Concavity of solutions to elliptic equations on the sphere\nby Ju
lian Scheuer (Cardiff University) as part of Online Seminar "Geometric Ana
lysis"\n\n\nAbstract\nAn important question in PDE is when a solution to a
n elliptic\nequation is concave. This has been of interest with respect to
the spectrum of\nlinear equations as well as in nonlinear problems. An ol
d technique going back\nto works of Korevaar\, Kennington and Kawohl is to
study a certain two-point\nfunction on a Euclidean domain to prove a so-c
alled concavity maximum principle\nwith the help of a first and second der
ivative test. To our knowledge\, so far\nthis technique has never been tra
nsferred to other ambient spaces\, as the\nnonlinearity of a general ambie
nt space introduces geometric terms into the\nclassical calculation\, whic
h in general do not carry a sign. In this talk we\nhave a look at this sit
uation on the unit sphere. We prove a concavity maximum\nprinciple for a b
road class of degenerate elliptic equations via a careful\nanalysis of the
spherical Jacobi fields and their derivatives. In turn we obtain\nconcavi
ty of solutions to this class of equations. This is joint work with Mat\nL
angford\, University of Tennessee Knoxville.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Bamler (UC Berkeley)
DTSTART:20200818T170000Z
DTEND:20200818T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/24
DESCRIPTION:Title: Ricci flow in higher dimensions\nby Richard Bamler (UC Berkeley)
as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nI will prese
nt new results concerning Ricci flows in higher dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Engelstein
DTSTART:20200825T170000Z
DTEND:20200825T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/25
DESCRIPTION:Title: Winding for Wave Maps\nby Max Engelstein as part of Online Semina
r "Geometric Analysis"\n\n\nAbstract\nWave maps are harmonic maps from a L
orentzian domain to a\nRiemannian target. Like solutions to many energy cr
itical PDE\, wave maps can\ndevelop singularities where the energy concent
rates on arbitrary small\nscales but the norm stays bounded. Zooming in on
these singularities yields\na harmonic map (called a soliton or bubble) i
n the weak limit. One\nfundamental question is whether this weak limit is
unique\, that is to say\,\nwhether different bubbles may appear as the lim
it of different sequences of\nrescalings.\n\nWe show by example that uniqu
eness may not hold if the target manifold is\nnot analytic. Our construc
tion is heavily inspired by Peter Topping's\nanalogous example of a ``wind
ing" bubble in harmonic map heat flow. However\,\nthe Hamiltonian nature o
f the wave maps will occasionally necessitate\ndifferent arguments. This
is joint work with Dana Mendelson (U Chicago).\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter McGrath (North Carolina State University)
DTSTART:20200901T170000Z
DTEND:20200901T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/26
DESCRIPTION:Title: Quantitative Isoperimetric Inequalities on Riemannian Surfaces\nb
y Peter McGrath (North Carolina State University) as part of Online Semina
r "Geometric Analysis"\n\n\nAbstract\nTalk Abstract: In this talk\, we in
troduce a scattering asymmetry which measures the asymmetry of a domain by
quantifying its incompatibility with an isometric circle action. We prov
e a quantitative isoperimetric inequality involving the scattering asymmet
ry and characterize the domains with vanishing scattering asymmetry by the
ir rotational symmetry. We also give a new proof of the sharp Sobolev ine
quality for Riemannian surfaces which is independent of the isoperimetric
inequality. This is joint work with J. Hoisington.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Alvarado (Amherst College)
DTSTART:20200908T170000Z
DTEND:20200908T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/27
DESCRIPTION:Title: A characterization of the Sobolev embedding theorem in metric-measure
spaces.\nby Ryan Alvarado (Amherst College) as part of Online Seminar
"Geometric Analysis"\n\n\nAbstract\nHistorically\, the Sobolev embedding
theorem on domains has played a key role in establishing many fundamental
results in the area of analysis and it is well known that the geometry of
the underlying domain is intimately linked to the availability of these em
beddings. In fact\, certain geometrical characterizations of domains which
support Sobolev embeddings have been obtained in the Euclidean setting. I
n this talk\, we will revisit these embedding theorems in the more general
context of metric-measure spaces and discuss some recent work which ident
ifies a measure theoretic condition that is both necessary and sufficient
to ensure their veracity. A measure characterization of Sobolev extension
domains in the metric setting as well as applications of our methods to sp
aces supporting $p$-Poincaré inequalities will also be discussed. This ta
lk is based on joint work with Przemysław Górka (Warsaw University of Te
chnology)\, Piotr Hajłasz (University of Pittsburgh).\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fritz Hiesmayr (University College London)
DTSTART:20200922T170000Z
DTEND:20200922T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/29
DESCRIPTION:Title: A rigidity theorem for the Allen-Cahn equation in $S^3$\nby Fritz
Hiesmayr (University College London) as part of Online Seminar "Geometric
Analysis"\n\n\nAbstract\nWe present a recent rigidity theorem for the All
en-Cahn equation in the three-sphere: critical points with Morse index are
symmetric and vanish on a Clifford torus. One key ingredient is a novel F
rankel-type property we establish for the nodal sets of any two distinct s
olutions: they intersect if they are connected. This in fact holds in all
manifolds with positive Ricci curvature. Time permitting we will discuss a
dditional rigidity results in higher-dimensional spheres.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Maddocks (EPF Lausanne)
DTSTART:20201124T180000Z
DTEND:20201124T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/31
DESCRIPTION:Title: Ideal knots: The trefoil\, analysis and numerics to experiment\nb
y John Maddocks (EPF Lausanne) as part of Online Seminar "Geometric Analys
is"\n\n\nAbstract\nGeometrical knot theory is an area of mathematics that
has been growing in\nactivity over the last few decades. It involves the s
tudy of specific shapes\nof knotted curves\, rather than their topology\,
where the specific knot shape\nis fixed by some criterion\, typically mini
mizing some form of knot energy.\nIn this talk I will introduce some older
work of both my collaborators and\nI\, as well as others\, on the speci
fic case of ideal\, or tightest\, knot\nshapes. I will start by explaining
the analytical difficulties\, along with\nsome associated theorems. Then
I will describe some numerical results\nconcentrating on the specific case
of the ideal trefoil. And finally I will\ndescribe some very recent exper
imental results for the ideal trefoil\nobtained by the group of Pedro Reis
at the EPFL.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marius Müller (Albert-Ludwigs-Universität Freiburg)
DTSTART:20201201T180000Z
DTEND:20201201T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/32
DESCRIPTION:Title: The Willmore Flow of Tori of Revolution\nby Marius Müller (Alber
t-Ludwigs-Universität Freiburg) as part of Online Seminar "Geometric Anal
ysis"\n\n\nAbstract\nThis is a joint work with Anna Dall'Acqua\, Adrian Sp
ener and Reiner Schätzle. \n\nWe study the $\\textcolor{red}{\\textbf{Wil
lmore flow}}$ of tori that have a revolution symmetry - so-called tori of
revolution. Luckily\, the Willmore flow preserves this symmetry. Because o
f that we can look at the flow as an evolution of the "profile curves" - a
reduction of the dimension!\n\nWe will examine the geometry of this curve
evolution and understand why it is somewhat natural to look at those curv
es in $\\textcolor{red}{\\textbf{hyperbolic geometry}}$. We prove: \n\n$\\
textcolor{green}{ \\textbf{If the hyperbolic length of the profile curves
remains bounded\, then the Willmore flow converges.}}$\n\nThe remaining qu
estion: How can the hyperbolic length of those curves be controlled? We us
e variational methods to $\\textcolor{red}{\\textbf{control the hyperbolic
length}}$ by the Willmore energy - but this control is only available bel
ow an energy level of $\\textcolor{red}{\\mathbf{8\\pi}}$. We obtain:\n\n$
\\textcolor{green}{\\textbf{If we start the Willmore flow with a torus of
revolution of Willmore energy below $8\\pi$\, then the flow converges}.}$
\n\nIf time allows: The threshold of $8\\pi$ is also sharp and plays an im
portant role in the context of the Willmore functional. It is also the sam
e threshold that was already found by E. Kuwert and R. Schätzle for the W
illmore flow of spheres.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Siffert (Universität Münster)
DTSTART:20200929T170000Z
DTEND:20200929T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/33
DESCRIPTION:Title: Constructing explicit p-harmonic functions\nby Anna Siffert (Univ
ersität Münster) as part of Online Seminar "Geometric Analysis"\n\n\nAbs
tract\nThe study of $p$-harmonic functions on Riemannian manifolds has inv
oked the interest of mathematicians and physicists for nearly two centurie
s.\nApplications within physics can for example be found\nin continuum mec
hanics\, elasticity theory\, as well as two-dimensional hydrodynamics prob
lems involving Stokes flows of incompressible Newtonian fluids.\n\nIn my t
alk I will focus on the construction of explicit $p$-harmonic functions o
n rank-one Lie groups of Iwasawa type.\nThis joint work with Sigmundur Gud
mundsson and Marko Sobak.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renan Assimos (Leibniz Universitaet Hannover)
DTSTART:20201013T170000Z
DTEND:20201013T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/34
DESCRIPTION:Title: On a spherical Bernstein theorem by B. Solomon\nby Renan Assimos
(Leibniz Universitaet Hannover) as part of Online Seminar "Geometric Analy
sis"\n\n\nAbstract\nJoint work with J. Jost: A result of B.Solomon (On the
Gauss map of an area-minimizing hypersurface. 1984. Journal of Differenti
al Geometry\, 19(1)\, 221-232.) says that a compact minimal hypersurface $
M^k$ of the sphere $S^{k+1}$ with $H^1(M)=0$\, whose Gauss map omits a nei
ghborhood of an $S^{k−1}$ equator\, is totally geodesic in $S^{k+1}$. In
this talk\, I will present a new proof strategy for Solomon's theorem whi
ch allows us to obtain analogous results for higher codimensions. If time
permits\, we sketch the proof for codimension 2 compact minimal submanifol
ds of $S^{k+1}$.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Menzel (Universität Regensburg)
DTSTART:20201110T180000Z
DTEND:20201110T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/35
DESCRIPTION:Title: Boundary Value Problems for Evolutions of Willmore Type\nby Julia
Menzel (Universität Regensburg) as part of Online Seminar "Geometric Ana
lysis"\n\n\nAbstract\nThe Willmore flow arises as the $L^2$-gradient flow
of the Willmore energy which is itself given by the integrated squared mea
n curvature of the considered surface. \n\n\n\nAfter a short introduction
and review of known results on the Willmore flow of curves and closed surf
aces\, we discuss the existence of solutions to the Willmore flow of compa
ct open surfaces immersed in Euclidean space subject to Navier boundary co
nditions.\n\n\n\nWe further study the elastic flow of planar networks comp
osed of curves meeting in triple junctions. As a main result we obtain tha
t starting from a suitable initial network the flow exists globally in tim
e if the length of each curve remains uniformly bounded away from zero and
if at least one angle at each triple junction stays uniformly bounded awa
y from zero\, $\\pi$ and $2\\pi$.\n\n\n\nThis talk is based on my recently
submitted PhD thesis and includes joint work with H. Abels\, H. Garcke an
d A. Pluda.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Hirsch (University of Leipzig)
DTSTART:20201006T170000Z
DTEND:20201006T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/36
DESCRIPTION:Title: On the regularity of area minimzing currents mod(p)\nby Jonas Hir
sch (University of Leipzig) as part of Online Seminar "Geometric Analysis"
\n\n\nAbstract\njoint work with C. De Lellis\, A Marches and S. Stuvard\n\
nIn this talk I would like to give a glimpse on the regularity of area min
imzing currents mod(p).\n\nMotivation: If one considers real soap f
ilms one notice that from time to time one can find configurations where d
ifferent soap films join on a common piece. One possibility to allow this
kind of phenomenon is to consider flat chains with coefficients in $\\math
bb Z_p$. For instance for $p = 2$ one can deal with unoriented surfaces\,
for $p = 3$ one allows triple junctions.\n\nConsidering area minimzing cur
rents within this class the aim is to give a bound on the Hausdorff dimens
ion of the singular set sing(T) in the interior. These are alle points whe
re the precise representative of the minimiser T is not even locally suppo
rted on a piece of a $C^{1\,\\alpha}$ regular surface.
\nAfter a short
introduction into general theory of currents mod(p)\, I will give you glim
pse on the previously known results and on our new bound on the Hausdorff
dimension of the set. If time permits I will give a short outlook of what
we would be the expected result.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Brendle (Columbia University)
DTSTART:20201027T180000Z
DTEND:20201027T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/37
DESCRIPTION:Title: The isoperimetric inequality for minimal surfaces\nby Simon Brend
le (Columbia University) as part of Online Seminar "Geometric Analysis"\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Campbell (University of Hradec Kralove)
DTSTART:20201020T170000Z
DTEND:20201020T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/38
DESCRIPTION:Title: Pathological Sobolev homeomorphisms in GFT and NE\nby Daniel Camp
bell (University of Hradec Kralove) as part of Online Seminar "Geometric A
nalysis"\n\n\nAbstract\nSobolev homeomorphisms are the natural choice for
minimization problems in non-linear elasticity. For the regularity of thes
e problems it would be useful to be able to approximate these maps by smoo
th homeomorphisms in their corresponding Sobolev space (the so-called Ball
-Evans problem). We construct a pair of homeomorphisms for which is imposs
ible simultaneously solving the Hajlasz problem. That is we construct a So
bolev homeomorphism equalling identity on the boundary of a cube but with
negative Jacobian almost everywhere.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ursula Ludwig (University of Duisburg-Essen)
DTSTART:20201208T180000Z
DTEND:20201208T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/39
DESCRIPTION:Title: An Extension of a Theorem by Cheeger and Müller to Spaces with Isola
ted Conical Singularities\nby Ursula Ludwig (University of Duisburg-Es
sen) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nAn impo
rtant comparison theorem in global analysis is the comparison of analytic
and topological torsion for smooth compact manifolds equipped with a unita
ry flat vector bundle. It has been conjectured by Ray and Singer and has b
een independently proved by Cheeger and Mu ̈ller in the 70ies. Bismut and
Zhang combined the Witten deformation and local index techniques to gener
alise the result of Cheeger and Mu ̈ller to arbitrary flat vector bundles
with arbitrary Hermitian metrics. The aim of this talk is to present an e
xtension of the Cheeger-Mu ̈ller theorem to spaces with isolated conical
singularities by generalising the proof of Bismut and Zhang to the singula
r setting.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Behnam Esmayli (Uni of Pittsburgh)
DTSTART:20201117T180000Z
DTEND:20201117T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/40
DESCRIPTION:Title: Co-area formula for maps into metric spaces\nby Behnam Esmayli (U
ni of Pittsburgh) as part of Online Seminar "Geometric Analysis"\n\n\nAbst
ract\nCo-area formula for maps between Euclidean spaces contains\, as its
very special cases\, both Fubini's theorem and integration in polar coordi
nates formula. In 2009\, L. Reichel proved the coarea formula for maps fro
m Euclidean spaces to general metric spaces. I will discuss a new proof of
the latter by the way of an implicit function theorem for such maps. An i
mportant tool is an improved version of the coarea inequality (a.k.a Eilen
berg inequality) that was the subject of a recent joint work with Piotr Ha
jlasz. Our proof of the coarea formula does not use the Euclidean version
of it and can thus be viewed as a new (and arguably more geometric) proof
in that case as well.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hermann Karcher (University of Bonn)
DTSTART:20201215T180000Z
DTEND:20201215T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/41
DESCRIPTION:Title: Numerical experiments with closed constant curvature space curves
\nby Hermann Karcher (University of Bonn) as part of Online Seminar "Geome
tric Analysis"\n\n\nAbstract\nThe discovery story will be told with pictur
es illustrating all steps\, including the observation\nbelow whic
h we used but could not prove. Since the shape of space curves is difficul
t to be\ncorrectly deduced from planar images\, most images will be red-g
reen anaglyphs. They\ncan be looked at without red-green glasses\, but wit
hout giving the 3D impression.\n\nDec 15\,2020: H. Karcher: Closed
constant curvature space curves\n\nThe only closed constant curv
ature space curves which I knew in 2004\nwere made from pieces of circles
and helices.\nThe Frenet equations allow to construct space curves of cons
tant curvature $\\kappa$\nby prescribing a torsion function $\\tau(s)$. Fo
r closed curves one needs periodic\ntorsion functions\, for example Fourie
r polynomials. If one chooses these\nfunctions so that they are skew symme
tric with respect to their zeros\, $\\tau(a-s)=-\\tau(a+s)$\, then\nthe re
sulting curves have the normal planes at these points as planes of\nmirror
symmetry. If adjacent symmetry planes have angles such as $\\pi/3$\,\nthe
n the curves are forced by their symmetries to be closed. This gives the \
nfirst collection of new examples.\n\nIf the torsion functions are even wi
th respect to their extremal points\, i.e.\n$\\tau(a-s) = \\tau(a+s)$\, th
en the resulting curves have their principal normals\nat these points as s
ymmetry axes for $180^\\circ$ rotations. If two such adjacent\nsymmetry no
rmals are coplanar and intersect under rational angles
($\\pi p/q$)\,
\nthen the curves are again forced by their symmetries to close up. Theref
ore\none can hope to get examples by solving a 2-parameter problem.\n\nThi
s is made simple by an observation which I cannot prove: The dist
ance of\nadjacent symmetry normals depends in a surprisingly monotone way
on the constant\nterm in the Fourier polynomial $\\tau(s) = b_0 + b_1\\\,
\\sin(s) + b_3\\\, \\sin(3s)$. This\nallows to consider $b_0 = b_0(\\kappa
\, b_1\, b_3)$\, such that the symmetry normals of the\nresulting curves a
re coplanar and hence intersect all in one point. Therefore we\nhave again
to solve a 1-parameter problem by choosing $\\kappa\, b_1\, b_3$ in such
a way\nthat adjacent symmetry normals intersect with a rational angle. Thi
s gives a wealth\nof new examples.\n\nThe evolutes of such curves have als
o constant curvature $\\kappa$\, but they have \nsingularities at the zero
s of $\\tau(s)$. This led to a search for closed examples with $\\tau(s) >
0$.\nA (2-11)-torus knot showed up and suggested to look for examples on
tori. Easy ones\nare again found by symmetries and more complicated ones a
s solutions of intermediate\nvalue problems. The formulas work also on cyl
inders and revealed easier examples than\nall the previous ones!\n\nThen E
. Tjaden suggested to look for examples which are congruent to their evolutes.\nThey were found by modifying the Frenet equations.
The $(2\, 2n+1)$- torus knots among\nthem are in fact their own evolutes.\
n
LOCATION:https://stable.researchseminars.org/talk/OSGA/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Weth (Goethe University Frankfurt)
DTSTART:20210126T180000Z
DTEND:20210126T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/42
DESCRIPTION:Title: Critical domains for the first nonzero Neumann eigenvalue in Riemanni
an manifolds\nby Tobias Weth (Goethe University Frankfurt) as part of
Online Seminar "Geometric Analysis"\n\n\nAbstract\nThe talk is concerned w
ith geometric optimization problems related to the Neumann eigenvalue prob
lem for the Laplace-Beltrami operator on bounded subdomains of a Riemannia
n manifold. More precisely\, we analyze locally extremal domains for the f
irst nontrivial eigenvalue with respect to volume preserving domain pertu
rbations\, and we show that corresponding notions of criticality arise in
the form of overdetermined boundary value problems. Our results rely on an
extension of Zanger's shape derivative formula which covers the case wher
e the first nonzero Neumann eigenvalue is not simple. In the second part o
f the talk\, we focus on product manifolds with euclidean factors\, and we
classify the subdomains where the associated overdetermined boundary valu
e problem has a solution. If time permits\, I will also briefly discuss th
e first nontrivial Stekloff eigenvalue. \nThis is joint work with Moustaph
a Fall (AIMS Senegal).\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilderich Tuschmann (Karlsruhe Institute of Technology)
DTSTART:20210119T180000Z
DTEND:20210119T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/43
DESCRIPTION:Title: Spaces and Moduli Spaces of Riemannian Metrics\nby Wilderich Tusc
hmann (Karlsruhe Institute of Technology) as part of Online Seminar "Geome
tric Analysis"\n\n\nAbstract\nConsider a smooth manifold with a Riemannian
metric satisfying some sort of curvature constraint like\, for example\,
positive scalar curvature\, non-negative Ricci or negative sectional curva
ture\, being Einstein\, Kähler\, Sasaki\, etc. A natural question to stud
y is then what the space of all such metrics does look like. Moreover\, on
e can also pose this question for corresponding moduli spaces of metrics\,
i.e.\, quotients of the former by (suitable subgroups of) the diffeomorph
ism group of the manifold\, acting by pulling back metrics. \n\nThese spac
es are customarily equipped with the topology of smooth convergence on com
pact subsets and the quotient topology\, respectively\, and their topologi
cal properties then provide the right means to measure 'how many' differen
t metrics and geometries the given manifold actually does exhibit\; but on
e can topologize and view those also in very different manners.\n\nIn my t
alk\, I will report on some general results and open questions about space
s and moduli spaces of metrics with non-negative Ricci or sectional curvat
ure as well as other lower curvature bounds on closed and open manifolds\,
and\, in particular\, also discuss broader non-traditional approaches fro
m metric geometry and analysis to these objects and topics.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrik Matthiesen (University of Chicago)
DTSTART:20201103T181500Z
DTEND:20201103T191500Z
DTSTAMP:20260404T110912Z
UID:OSGA/44
DESCRIPTION:Title: New minimal surfaces from shape optimization\nby Henrik Matthiese
n (University of Chicago) as part of Online Seminar "Geometric Analysis"\n
\n\nAbstract\nI will discuss the connection between sharp eigenvalue bound
s and minimal surfaces in two cases:\nThe first eigenvalue of the Laplacia
n on a closed surface among unit area metrics\, and\nthe first Steklov eig
envalue on a compact surface with non empty boundary among metrics with un
it length boundary.\nIn both cases maximizing metrics - if they exist - ar
e induced by certain minimal immersions.\nMore precisely\, minimal immersi
ons into round spheres for the closed case and free boundary minimal immer
sions into Euclidean balls in the bordered case.\nI will discuss the solut
ion of the existence problem for maximizers in both these cases\, which pr
ovides many new examples of minimal surfaces of the aforementioned types.\
nThis is based on joint work with Anna Siffert in the closed case and Roma
in Petrides in the bordered case.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rupert Frank
DTSTART:20210112T180000Z
DTEND:20210112T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/45
DESCRIPTION:Title: Which magnetic fields support a zero mode?\nby Rupert Frank as pa
rt of Online Seminar "Geometric Analysis"\n\n\nAbstract\nMotivated by the
question from mathematical physics about the size of magnetic fields that
support zero modes for the three dimensional Dirac equation\, we study a c
ertain conformally invariant spinor equation. We state some conjectures an
d present some results supporting them. Those concern\, in particular\, tw
o novel Sobolev inequalities for spinors and vector fields.\n\nThe talk is
based on joint work with Michael Loss.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Creutz (University of Cologne)
DTSTART:20210202T180000Z
DTEND:20210202T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/46
DESCRIPTION:Title: Area minimizing surfaces for singular boundary values\nby Paul Cr
eutz (University of Cologne) as part of Online Seminar "Geometric Analysis
"\n\n\nAbstract\nFix a nonnegative integer g and a finite configuration of
disjoint Jordan curves in Euclidean space. Then\, by a classical result o
f Douglas\, there is an area minimizer among all surfaces of genus at most
g which span the given curve configuration. In the talk I will discuss a
generalization of this theorem to singular configurations of possibly non-
disjoint or self-intersecting curves. The proof relies on an existence res
ult for minimal surfaces in singular metric spaces and does not seem amena
ble within classical smooth techniques.\n\nThis is joint work with M. Fitz
i.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Litzinger (Queen Mary College)
DTSTART:20210209T180000Z
DTEND:20210209T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/47
DESCRIPTION:Title: Optimal regularity for Pfaffian systems and the fundamental theorem o
f surface theory\nby Florian Litzinger (Queen Mary College) as part of
Online Seminar "Geometric Analysis"\n\n\nAbstract\nThe fundamental theore
m of surface theory asserts the existence of a surface immersion with pres
cribed first and second fundamental forms that satisfy the Gauss–Codazzi
–Mainardi equations. Its proof is based on the solution of a Pfaffian sy
stem and an application of the Poincaré lemma. Consequently\, the regular
ity of the resulting immersion crucially depends on the regularity of the
solution of the corresponding Pfaffian system. This talk shall briefly rev
iew both the classical smooth case and the regularity theory and then intr
oduce an extension to the optimal regularity.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerhard Huisken (University of Tübingen)
DTSTART:20210216T180000Z
DTEND:20210216T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/48
DESCRIPTION:Title: Mean curvature flow with surgery\nby Gerhard Huisken (University
of Tübingen) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract
\nThe evolution of hypersurfaces in a Riemannian manifold along its mean c
urvature vector is governed by a quasilinear parabolic system that exhibit
s smoothing behavior and singularity formation at the same time since the
evolution of the geometry is governed by a non-linear reaction diffusion s
ystem. The lecture explains how for embedded 2-surfaces of positive mean c
urvature in general ambient manifolds long-time solutions can be construct
ed that contain finitely many surgeries near singular regions. Finally we
discuss applications in Geometry and General Relativity.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephan Wojtowytsch (Princeton University)
DTSTART:20210223T180000Z
DTEND:20210223T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/49
DESCRIPTION:Title: Optimal transport for non-convex optimization in machine learning
\nby Stephan Wojtowytsch (Princeton University) as part of Online Seminar
"Geometric Analysis"\n\n\nAbstract\nFunction approximation is a classical
task in both classical numerical analysis and machine learning. Elements o
f the recently popular class of neural networks depend nonlinearly on a fi
nite set of parameters. This nonlinearity gives the function class immense
approximation power\, but causes parameter optimization problems to be no
n-convex. In fact\, generically the set of global minimizers is a (curved)
manifold of positive dimension. Despite this non-convexity\, gradient des
cent based algorithms empirically find good minimizers in many application
s. We discuss this surprising success of simple optimization algorithms fr
om the perspective of Wasserstein gradient flows in the case of shallow ne
ural networks in the infinite parameter limit.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruijun Wu (SISSA\, Trieste)
DTSTART:20210302T180000Z
DTEND:20210302T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/50
DESCRIPTION:Title: Super Liouville equations on the 2-sphere\nby Ruijun Wu (SISSA\,
Trieste) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nThe
2D super Liouville equations\, from the super Liouville field theory\, is
a conformally invariant system which couples the classical Liouville equa
tion with a Dirac equation. We are interested in the existence of nontrivi
al solutions. Aside from those known solutions induced from prescribing cu
rvature equations and those from Killing spinors\, we introduced an additi
onal (but natural) parameter and obtained new solutions via bifurcation th
eory. This is a joint work with A. Malchiodi and A. Jevnikar.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Ketterer (University of Toronto)
DTSTART:20210309T180000Z
DTEND:20210309T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/51
DESCRIPTION:Title: Inscribed radius bounds for metric measure spaces with mean-H-convex
boundary\nby Christian Ketterer (University of Toronto) as part of Onl
ine Seminar "Geometric Analysis"\n\n\nAbstract\nWe introduce a synthetic l
ower mean curvature bound for the\ntopological boundary of a subset in a m
etric measure space that satisfies a\nlower Ricci curvature bound in the s
ense of Lott\, Sturm and Villani. This \nlower mean curvature bound coi
ncides with the classical notion in smooth\ncontext. As application I pres
ent a theorem about sharp comparison estimates\nfor the inscribed radius o
f such subsets. Moreover\, in the context of\nRCD(0\,N) metric measure s
paces (Riemannian curvature-dimension condition)\nequality holds if and on
ly if the subset is isometric to a geodesic ball\ncentered at the tip of a
n Euclidean cone. This generalizes theorems in\nsmooth context by Kasue an
d Sakurai to a singular framework. This is a joint\nwork with Annegret Bur
tscher\, Robert McCann and Eric Woolgar.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Verena Bögelein (University Salzburg\, Austria)
DTSTART:20210316T180000Z
DTEND:20210316T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/52
DESCRIPTION:Title: Higher regularity in congested traffic dynamics\nby Verena Bögel
ein (University Salzburg\, Austria) as part of Online Seminar "Geometric A
nalysis"\n\n\nAbstract\nWe consider an elliptic system that is motivated b
y a congested traffic dynamics problem. It has the form\n$$\n \\mathrm{div
}\\bigg((|Du|-1)_+^{p-1}\\frac{Du}{|Du|}\\bigg)=f\,\n$$\nand falls into th
e context of very degenerate problems. Continuity properties of the gradie
nt have been investigated in the scalar case by Santambrogio & Vespri and
Colombo & Figalli. \nIn this talk we establish the optimal regularity of
weak solutions in the vectorial case for any $p>1$. This is joint work wit
h F. Duzaar\, R. Giova and A. Passarelli di Napoli.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sonja Hohloch (University of Antwerp)
DTSTART:20210323T180000Z
DTEND:20210323T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/53
DESCRIPTION:Title: On recent advances in semitoric integrable systems\nby Sonja Hohl
och (University of Antwerp) as part of Online Seminar "Geometric Analysis"
\n\n\nAbstract\nRoughly speaking\, a semitoric system is a completely inte
grable Hamiltonian system on a 4-dimensional symplectic manifold that admi
ts only nondegenerate singularities without hyperbolic components and whos
e flow gives rise to an $(\\mathbb S^1 \\times \\mathbb R)$-action. Couple
d spin oscillators and coupled angular momenta are examples of such semito
ric systems.\n\nSemitoric systems have been symplectically classified abou
t a decade ago by Pelayo $\\&$ Vu Ngoc by means of five invariants. Recent
ly\, there has been made considerable progress by various authors concerni
ng the computation of these invariants.\n\nIn this talk\, we will give an
introduction to semitoric systems before considering a recent\, intuitive
family of semitoric systems that allows for explicit observation of bifurc
ation behaviour such as bifurcations between focus-focus and elliptic-elli
ptic singularities and other interesting geometric-topological features re
lated to singularities and bifurcations. The latter part is based on a joi
nt work with A.\\ De Meulenaere.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jimmy Scott (University of Pittsburgh)
DTSTART:20210330T170000Z
DTEND:20210330T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/54
DESCRIPTION:Title: Fractional Korn-Type Inequalities and Applications\nby Jimmy Scot
t (University of Pittsburgh) as part of Online Seminar "Geometric Analysis
"\n\n\nAbstract\nWe show that a class of spaces of vector fields whose sem
i-norms involve the magnitude of ``directional" difference quotients is in
fact equivalent to the class of fractional Sobolev-Slobodeckij spaces. Th
e equivalence can be considered a Korn-type characterization of said Sobol
ev spaces. For vector fields defined on various classes of domains\, we ob
tain a relevant form of the inequality. As an application\, we consider va
riational problems associated to strongly coupled systems of nonlocal equa
tions motivated by a continuum mechanics model known as peridynamics. We u
se the fractional Korn-type inequalities to characterize vector fields in
associated energy spaces and obtain existence and uniqueness of solutions
in fractional Sobolev spaces.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oded Stein (MIT)
DTSTART:20210406T170000Z
DTEND:20210406T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/55
DESCRIPTION:Title: The Biharmonic Equation in Geometry Processing\nby Oded Stein (MI
T) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nThe Lapla
cian has been an extensively used tool of geometry processing and computer
graphics for a long time.\nIn this talk we will take a look at a close re
lative of the Laplacian\, the Bilaplacian\, as well as its partial differe
ntial equation\, the biharmonic equation.\nThe Bilaplacian can be used in
applications such as smoothing\, interpolation\, character animation\, dis
tance computation\, and more.\nWe will examine the biharmonic equation and
its use in geometry processing\, we will look at ways to discretize it fo
r curved surfaces\, and we will discuss different boundary conditions of t
he biharmonic equation.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amy Novick-Cohen (Technion-IIT\, Haifa)
DTSTART:20210413T170000Z
DTEND:20210413T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/56
DESCRIPTION:Title: Surface diffusion\, and surface diffusion coupled with mean curvature
motion\nby Amy Novick-Cohen (Technion-IIT\, Haifa) as part of Online
Seminar "Geometric Analysis"\n\n\nAbstract\nSurface diffusion as well as m
ean curvature motion constitute geometric motions relevant to the modellin
g various phenomena arising in modeling thin poly-crystalline films. We fi
rst review some special grooving solutions and traveling wave solutions. A
fterwards we focus on certain composite axi-symmetric geometries\; here th
e steady states may be described by piecing together Delaunay surfaces\, a
nd related evolutionary questions are pertinent to solid state wetting and
dewetting.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Malchiodi (Scuola Normale Superiore)
DTSTART:20210420T170000Z
DTEND:20210420T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/57
DESCRIPTION:Title: On critical points of the Moser-Trudinger functional\nby Andrea M
alchiodi (Scuola Normale Superiore) as part of Online Seminar "Geometric A
nalysis"\n\n\nAbstract\nIt is known that in two dimensions Sobolev functio
ns in $W^{1\,2}$ satisfy critical embedding properties of exponential type
. In 1971 Moser obtained a sharp form of the embedding\, controlling the i
ntegrability of $F(u) := \\int \\exp(u^2)$ in terms of the Sobolev norm of
$u$.\nOn a closed Riemannian surface\, $F(u)$ is unbounded above for $\\|
u\\|_{W^{1\,2}} > 4 \\pi$. \nWe are however able to find critical points o
f $F$ constrained to any sphere \n$\\{ \\|u\\|_{W^{1\,2}} = \\beta \\}$\,
with $\\beta > 0$ arbitrary. The proof combines min-max theory\, a monoton
icity argument by Struwe\, blow-up analysis and compactness estimates. Thi
s is joint work with F. De Marchis\, O. Druet\, L. Martinazzi and P. D. Th
izy.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Palmurella (ETH Zürich)
DTSTART:20210427T170000Z
DTEND:20210427T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/58
DESCRIPTION:Title: The parametric approach to the Willmore flow\nby Francesco Palmur
ella (ETH Zürich) as part of Online Seminar "Geometric Analysis"\n\n\nAbs
tract\nWe introduce a parametric framework for the study of Willmore gradi
ent flows\nwhich enables to consider a general class of weak\, energy-leve
l solutions and opens\nthe possibility to study energy quantization and fi
nite-time singularities.\nIn this first work we restricted to a small-ener
gy regime and proved that\, for small-energy weak\nimmersions\, the Cauchy
problem in this class admits a unique solution.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Duzaar (University Erlangen-Nürnberg)
DTSTART:20210504T170000Z
DTEND:20210504T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/59
DESCRIPTION:Title: Higher integrability for porous medium type systems\nby Frank Duz
aar (University Erlangen-Nürnberg) as part of Online Seminar "Geometric A
nalysis"\n\n\nAbstract\nIn this talk we report on recent developments conc
erning the higher integrability\nof the spatial gradient to porous medium
type systems of the form\n$$\n \\partial_ t u- \\Delta(|u|^{m-1}u) = \\rm{
div}\\\, F.\n$$\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans Knüpfer (University of Heidelberg)
DTSTART:20210511T170000Z
DTEND:20210511T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/60
DESCRIPTION:Title: Gamma-limit for zigzag walls in thin ferromagnetic films\nby Hans
Knüpfer (University of Heidelberg) as part of Online Seminar "Geometric
Analysis"\n\n\nAbstract\nIn the continuum theory\, the magnetization of a
ferromagnetic sample $\\Omega \\subset \\R^3$ is described by a unit vecto
r field $m \\in H^1(\\Omega\,S^2)$. The minimization of the underlying mic
romagnetic energy leads to the formation of extended magnetic domains wit
h uniform magnetization\, separated by thin transition layers. One type of
such transition layers\, observed in thin ferromagnetic films are the so
called zigzag walls. We consider the family of energies\n$$E_\\varepsilon[
m] \\ = \\ \\frac{\\epsilon}{2}\\|\\nabla m\\|_{L^2(\\Omega)}^2 + \\frac 1
{2\\varepsilon} \\|m \\cdot e_2\\|_{L^2(\\Omega)}^2 %\n + \\frac{\\pi\\
lambda}{2|\\ln \\varepsilon|} \\|\\nabla \\cdot (m-M)\\|_{\\dot H^{-\\frac
12}}^2\, \n$$\nvalid for thin ferromagnetic films. We consider a mate
rial in the form a thin strip and\n enforce a charged domain wall by suit
able boundary conditions on $m$. Here\, $M$ is an arbitrary fixed backgro
und field to ensure global neutrality of magnetic charges. In the\n limit
$\\varepsilon \\to 0$ and for fixed $\\lambda > 0$\, corresponding to the
macroscopic\n limit\, we show that the energy $\\Gamma$--converges to a
limit energy where jump\n discontinuities of the magnetization are penali
zed anisotropically. In\n particular\, in the subcritical regime $\\lambd
a \\leq 1$ one--dimensional charged\n domain walls are favorable\, in the
supercritical regime $\\lambda > 1$ the limit\n model allows for zigzagi
ng two--dimensional domain walls.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Bandle (University Basel)
DTSTART:20210518T170000Z
DTEND:20210518T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/61
DESCRIPTION:Title: Domain variations for boundary value problems.\nby Catherine Band
le (University Basel) as part of Online Seminar "Geometric Analysis"\n\n\n
Abstract\nWe consider boundary value problems which are Euler-Lagrange equ
ations of certain energy-functionals. Important questions in this context
are: How do they depend on the geometry of the domain on which they are de
fined? For instance\, does the energy assume a minimum among all domains o
f given volume? How does the optimal region\, if it exists\, look like? \n
\nThe technique of domain variations studies the changes of functionals un
der infinitesimal deformations. It is a differential calculus that allows
to derive necessary conditions for the geometry of an optimal domain. Its
beginnings go back to Hadamard in 1908\, who calculated the first variatio
n of Green's functions with Dirichlet boundary conditions. In this talk\,
the first and second variations of the energy of torsion problem with Robi
n boundary conditions will be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sun-Yung Alice Chang (Princeton University)
DTSTART:20210525T170000Z
DTEND:20210525T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/62
DESCRIPTION:Title: On bi-Lipschitz equivalence of a class of non-conformally flat sphere
s\nby Sun-Yung Alice Chang (Princeton University) as part of Online Se
minar "Geometric Analysis"\n\n\nAbstract\nThis is a report of some recent
joint work with Eden Prywes and Paul Yang. The main\nresult is a bi-Lipsch
itz equivalence of a class of metrics on 4-shpere under curvature constrai
nts. The proof involves two steps: first a construction of quasiconformal
maps between\ntwo conformally related metrics in a positive Yamabe class\,
followed by the step of applying\nthe Ricci flow to establish the bi-Lips
chitz equivalence from such a conformal class to the\nstandard conformal c
lass on 4-spheres.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shankar Venkataramani (University of Arizona)
DTSTART:20210601T170000Z
DTEND:20210601T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/63
DESCRIPTION:Title: On branch points and C^{1\,1} pseudospherical immersions\nby Shan
kar Venkataramani (University of Arizona) as part of Online Seminar "Geome
tric Analysis"\n\n\nAbstract\nThis is a report of joint work with Toby She
arman. The key result is that one can define a (local) winding number of t
he Gauss Map for $C^{1\,1}$ hyperbolic surfaces in $R^3$ and this degree i
s an obstruction for approximation by smooth immersions in $W^{2\,2}_{loc}
$. I will discuss the ideas behind the proof\, as well as the motivation f
or studying this question\, which comes from the mechanics of non-Euclidea
n plates.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sigurd Angenent (University of Wisconsin–Madison)
DTSTART:20210608T170000Z
DTEND:20210608T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/64
DESCRIPTION:Title: Nonuniqueness in mean curvature flow and Ricci flow\nby Sigurd An
genent (University of Wisconsin–Madison) as part of Online Seminar "Geom
etric Analysis"\n\n\nAbstract\nReporting on joint work with Ilmanen and Ve
lazquez\, I will present examples of smooth solutions to MCF in $\\mathbb
R^{d}$ with $d\\in\\{4\, 5\, 6\, 7\, 8\\}$ that form a conical singularity
after which they allow many different forward smooth continuations. I wi
ll also show similar results obtained with Knopf concerning the Ricci flow
in dimensions $5\, \\dots\, 9$.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Rumpf (University of Bonn)
DTSTART:20210615T170000Z
DTEND:20210615T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/65
DESCRIPTION:Title: Riemannian calculus in shape spaces\nby Martin Rumpf (University
of Bonn) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nSpa
ces of curves and surfaces or spaces of images are considered as Riemannia
n manifolds.\nThe talk will develop a calculus on such spaces\, which enab
les\n\n- the computation of distances via minimizing a Riemannian pa
th energy\,
\n- interpolation of shapes along geodesic paths\,
\
n- extrapolation via the Riemannian exponential map\,
\n- detail t
ransfer via parallel transport\,
\n- key pose interpolation via Riem
annian splines\, and
\n- statistical analysis via Riemannian PCA.\n
\nTo this end a time discrete calculus is introduced and its\ncon
vergence is discussed.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans-Joachim Hein (University of Münster)
DTSTART:20210622T170000Z
DTEND:20210622T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/66
DESCRIPTION:Title: Smooth asymptotics for collapsing Calabi-Yau metrics\nby Hans-Joa
chim Hein (University of Münster) as part of Online Seminar "Geometric An
alysis"\n\n\nAbstract\nYau's solution of the Calabi conjecture provided th
e first nontrivial examples of Ricci-flat Riemannian metrics on compact ma
nifolds. Attempts to understand the degeneration patterns of these metrics
in families have revealed many remarkable phenomena over the years. I wil
l review some aspects of this story and present recent joint work with Val
entino Tosatti where we obtain a complete asymptotic expansion (locally un
iformly away from the singular fibers) of Calabi-Yau metrics collapsing al
ong a holomorphic fibration of a fixed compact Calabi-Yau manifold. This r
elies on a new analytic method where each additional term of the expansion
arises as the obstruction to proving a uniform bound on one additional de
rivative of the remainder.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Bernig (Goethe University Frankfurt)
DTSTART:20210706T170000Z
DTEND:20210706T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/67
DESCRIPTION:Title: Intrinsic volumes on pseudo-Riemannian manifolds\nby Andreas Bern
ig (Goethe University Frankfurt) as part of Online Seminar "Geometric Anal
ysis"\n\n\nAbstract\nThe intrinsic volumes in Euclidean space can be defin
ed via Steiner's tube formula and were characterized by Hadwiger as the un
ique continuous\, translation and rotation invariant valuations. By the We
yl principle\, their extension to Riemannian manifolds behaves naturally u
nder isometric embeddings.\n\nIn a series of papers with Dmitry Faifman an
d Gil Solanes\, we developed a theory of intrinsic volumes in pseudo-Eucli
dean spaces and on pseudo-Riemannian manifolds. Fundamental results like H
adwiger's theorem\, Weyl's principle and Crofton formulas on spheres have
their natural analogues in the pseudo-Riemannian setting.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerome Wettstein (ETH Zurich)
DTSTART:20211123T180000Z
DTEND:20211123T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/68
DESCRIPTION:Title: Properties of the Half-Harmonic Gradient Flow\nby Jerome Wettstei
n (ETH Zurich) as part of Online Seminar "Geometric Analysis"\n\n\nAbstrac
t\nIn this talk\, we discuss properties of the fractional harmonic gradien
t flow with values in $S^{n-1}$ and its generalisation to arbitrary target
manifolds\, as investigated by the speaker in . Particular attention is s
pent on comparing the non-local case with the local one\, i.e. the harmoni
c map flow.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Haslhofer (University of Toronto)
DTSTART:20210803T170000Z
DTEND:20210803T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/69
DESCRIPTION:Title: Mean curvature flow through neck-singularities\nby Robert Haslhof
er (University of Toronto) as part of Online Seminar "Geometric Analysis"\
n\n\nAbstract\nIn this talk\, I will explain our recent work showing that
mean curvature flow through neck-singularities is unique. The key is a cla
ssification result for ancient asymptotically cylindrical flows that descr
ibes all possible blowup limits near a neck-singularity. In particular\, t
his confirms Ilmanen’s mean-convex neighborhood conjecture\, and more pr
ecisely gives a canonical neighborhood theorem for neck-singularities. Fur
thermore\, assuming the multiplicity-one conjecture\, we conclude that for
embedded two-spheres mean curvature flow through singularities is well-po
sed. The two-dimensional case is joint work with Choi and Hershkovits\, an
d the higher-dimensional case is joint with Choi\, Hershkovits and White.\
n
LOCATION:https://stable.researchseminars.org/talk/OSGA/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans-Christoph Grunau (Otto-von-Guericke-Universität Magdeburg)
DTSTART:20210713T170000Z
DTEND:20210713T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/70
DESCRIPTION:Title: Boundary value problems for the Willmore and the Helfrich functional
for surfaces of revolution\nby Hans-Christoph Grunau (Otto-von-Guerick
e-Universität Magdeburg) as part of Online Seminar "Geometric Analysis"\n
\n\nAbstract\nThis talk concerns joint works with A. Dall'Acqua\, K. Decke
lnick\, M. Doemeland\, S. Eichmann\, and S. Okabe.\n\nA special form of t
he Helfrich energy for a sufficiently smooth (two dimensional) surface $
S \\subset \\mathbb{R} ^3 $ (with or without boundary) is defined by\n
$$\n {\\mathscr H}_\\varepsilon(S) := \\int_{S} H^2 \\\, d S + \\vare
psilon \\int_{S} \\\, d S \,\n $$\n where $H$ denotes the mean curva
ture of $S$.\n The first integral may be considered as a bending energy
and the second as\n surface (stretching) energy. ${\\mathscr W} (S):={
\\mathscr H}_0 (S)$ is\n called the Willmore functional.\n We consid
er surfaces of revolution $ S $\n $$\n (x\,\\varphi)\\mapsto \\
big(x\,u(x)\\cos \\varphi\, u(x)\\sin \\varphi \\big) \\\, \,\n \\q
uad x\\in[-1\,1]\,~\\varphi\\in[0\,2\\pi]\,\n $$\n with smooth stri
ctly positive profile curve $u$ subject to Dirichlet\n boundary conditi
ons\n $$\n u(-1)=\\alpha\,\\quad u(1)=\\beta\,\\quad u'(\\pm1)=0\n
$$\n and aim at minimising ${\\mathscr H}_\\varepsilon$. Thanks to th
ese boundary conditions the Gauss curvature integral $\\int_{S} K\\\, d S
$ becomes a constant and needs not to be considered.\n\nIn the first par
t of the lecture I shall consider the Willmore case\, i.e.\n $\\varepsi
lon=0$. After briefly recalling minimisation in the symmetric case\n $\
\alpha=\\beta$ (see [1\,4]) I shall show how much more complicated the pro
blem\n becomes for $\\alpha\\not=\\beta$. Only when $\\alpha$ and $\\be
ta$ do not differ\n too much\, the profile curve will remain a graph wh
ile in general it will\n become a nonprojectable curve\, see [3].\n\nIn
the second part\, ${\\mathscr H}_\\varepsilon$ is considered for\n $\\
varepsilon\\in[0\,\\infty)$\, but again in the symmetric setting $\\alpha
=\\beta$. For $\\alpha \\ge \\alpha_m = c_m \\cosh(\\frac{1}{c_m})\\approx
1.895$ with $c_m\\approx 1.564$ the unique solution of the equation\n$\n
\\frac{2}{c} = 1 + e ^ {-2/ c}\n$\, when one has a catenoid $v_\\alpha$
which globally minimises the surface\nenergy\, we find minimisers $u_\\v
arepsilon$ for any $\\varepsilon\\ge 0$\nand show uniform and locally smoo
th convergence $u_\\varepsilon \\to v_\\alpha$ under the singular limit\n$
\\varepsilon \\to \\infty$. These results are collected in [2].\n\nAt the
end I shall briefly mention recent work on obstacle problems [5].\n \n\n
\n \n[1] A. Dall'Acqua\, K. Deckelnick\, and H.-Ch. Grunau\,\
n Classical solutions to the Dirichlet problem for Willmore\n surfac
es of revolution\, Adv. Calc. Var. 1 (2008)\, 379-397.\n\n
[2] K. Deckelnick\, H.-Ch. Grunau\, and M. Doemeland\, Boundary value prob
lems for the Helfrich functional for surfaces of revolution\n - Exi
stence and asymptotic behaviour\, Calc. Var. Partial Differ. Equ.
60 (2021)\, Article number 32.\n\n[3] S. Eichmann and H.-Ch. Grun
au\,\n Existence for Willmore surfaces of revolution satisfying non-sym
metric Dirichlet boundary conditions\,\n Adv. Calc. Var. 12<
/b> (2019)\, 333–361.\n\n[4] H.-Ch. Grunau\, The asymptotic shape of a b
oundary layer of symmetric\n Willmore surfaces of revolution.\n In:
C. Bandle et al. (eds.)\, Inequalities and Applications 2010.\n Int
ernational Series of Numerical Mathematics 161 (2012)\, 19-29.
\n\n[5] H.-Ch. Grunau and S. Okabe\,\n Willmore obstacle problems under
Dirichlet boundary conditions\, submitted.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Cabre (ICREA and Universitat Politecnica de Catalunya)
DTSTART:20210720T170000Z
DTEND:20210720T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/71
DESCRIPTION:Title: Stable solutions to semilinear elliptic equations are smooth up to di
mension 9\nby Xavier Cabre (ICREA and Universitat Politecnica de Catal
unya) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nThe re
gularity of stable solutions to semilinear elliptic PDEs has been studied
since the 1970's. In dimensions 10 and higher\, there exist singular stabl
e energy solutions. In this talk I will describe a recent work in collabor
ation with Figalli\, Ros-Oton\, and Serra\, where we prove that stable sol
utions are smooth up to the optimal dimension 9. This answers to an open p
roblem posed by Brezis in the mid-nineties concerning the regularity of ex
tremal solutions to Gelfand-type problems.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Lamm (KIT)
DTSTART:20210914T170000Z
DTEND:20210914T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/73
DESCRIPTION:Title: Diffusive stability results for the harmonic map flow and related equ
ations\nby Tobias Lamm (KIT) as part of Online Seminar "Geometric Anal
ysis"\n\n\nAbstract\nThe goal of this talk is to introduce the audience to
the theory of diffusive stability in the context of the harmonic map flow
. This theory is useful when studying stability results for parabolic equa
tions and we will illustrate its use for geometric equations such as the h
armonic map flow.\nAdditionally\, we use this theory in order improve vari
ous uniqueness results for solutions with rough initial data.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jürgen Jost (MPI Leipzig)
DTSTART:20210727T170000Z
DTEND:20210727T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/74
DESCRIPTION:Title: Nonpositive curvature: Geometric and analytic aspects\nby Jürgen
Jost (MPI Leipzig) as part of Online Seminar "Geometric Analysis"\n\n\nAb
stract\nMotivated by questions from data analysis\, we develop a new appro
ach to curvature of metric spaces. The approach works also for discrete me
tric spaces and links curvature to deviations from hyperconvexity.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Waldron (University of Wisconsin - Madison)
DTSTART:20210810T170000Z
DTEND:20210810T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/75
DESCRIPTION:Title: Harmonic map flow for almost-holomorphic maps\nby Alex Waldron (U
niversity of Wisconsin - Madison) as part of Online Seminar "Geometric Ana
lysis"\n\n\nAbstract\nI'll describe some history\, recent results\, and op
en problems about harmonic map flow in dimension two.\n\nThe main result i
s as follows: let $\\Sigma$ be a compact oriented surface and $N$ a compac
t Kähler manifold with nonnegative holomorphic bisectional curvature (e.g
. $\\mathbb{CP}^n$). For harmonic map flow starting from an almost-holomor
phic map $\\Sigma \\to N$ (in the energy sense)\, the ``body map'' at each
singular time is continuous\, and no ``neck'' appears between the body ma
p and the bubble tree.\n\nThis is joint work with Chong Song.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio De Rosa (University of Maryland)
DTSTART:20210907T170000Z
DTEND:20210907T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/76
DESCRIPTION:Title: Regularity of anisotropic minimal surfaces\nby Antonio De Rosa (U
niversity of Maryland) as part of Online Seminar "Geometric Analysis"\n\n\
nAbstract\nI will present regularity theorems for weak minimal surfaces wi
th respect to anisotropic surface energies\, extending the celebrated isot
ropic counterparts proved by Allard.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Kusner (University of Massachusetts at Amherst)
DTSTART:20210629T170000Z
DTEND:20210629T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/77
DESCRIPTION:Title: ON THE CANHAM PROBLEM: BENDING ENERGY MINIMIZING SURFACES OF ANY GEN
US AND ISOPERIMETRIC RATIO\nby Rob Kusner (University of Massachusetts
at Amherst) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\
nIn 1970\, the biophysicist Peter CANHAM proposed that the shapes of red b
lood cells could be described variationally\, leading to the Canham proble
m: find the surfaces of genus $g$ embedded in $\\R^3$ that minimize their
Willmore bending energy $W=\\frac14 \\int H^2$ with given area and enclose
d volume\, or equivalently (since $W$ is scale invariant) with given isope
rimetric ratio $v \\in (0\, 1)$. Building on very recent work of Andrea MO
NDINO & Christian SCHARRER\, we solve the “existence” part of the prob
lem\; it suffices to find a comparison surface of genus $g$ with arbitrari
ly small isoperimetric ratio $v$ and $W < 8π$\, which we construct by glu
ing $g+1$ small catenoidal bridges to the bigraph of a singular solution f
or the linearized Willmore equation $∆(∆+2)φ = 0$ on the $(g+1)$-punc
tured sphere. (If time permits\, we may discuss our ongoing work to under
stand the “small $v$” limit\, as well as “uniqueness” aspects of t
he Canham problem.)\n\n— Rob KUSNER\, UMassAmherst & CoronavirusU\n\n[jo
int work with Peter MCGRATH\, NorthCarolinaStateU]\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Rupp (Ulm University)
DTSTART:20210824T170000Z
DTEND:20210824T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/78
DESCRIPTION:Title: A dynamic approach to the Canham problem\nby Fabian Rupp (Ulm Uni
versity) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nMot
ivated by the Canham-Helfrich model for lipid bilayers\, the minimization
of the Willmore energy among surfaces of given topological type subject to
the constraint of fixed isoperimetric ratio has been extensively studied
throughout the last decade. In this talk\, we consider a dynamical approac
h by introducing a non-local $L^2$-gradient flow for the Willmore energy\,
which preserves the isoperimetric ratio. For topological spheres with ini
tial energy below an explicit threshold\, we show global existence and con
vergence to a Helfrich immersion as $t\\to\\infty$. Our proof relies on a
blow-up procedure and a constrained version of the \nŁojasiewicz--Simon g
radient inequality.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodora Bourni (University of Tennessee\, Knoxville)
DTSTART:20210831T170000Z
DTEND:20210831T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/79
DESCRIPTION:Title: Ancient polygonal pancakes.\nby Theodora Bourni (University of Te
nnessee\, Knoxville) as part of Online Seminar "Geometric Analysis"\n\n\nA
bstract\nMean curvature flow (MCF) is the gradient flow of the area functi
onal\; it moves the surface in the direction of steepest decrease of area.
An important motivation for the study of MCF comes from its potential ge
ometric applications\, such as classification theorems and geometric inequ
alities. MCF develops ``singularities'' (curvature blow-up)\, which obstru
ct the flow from existing for all times and therefore understanding these
high curvature regions is of great interest. This is done by studying anc
ient solutions\, solutions that have existed for all times in the past\, a
nd which model singularities. In this talk we will discuss their importanc
e and ways of constructing and classifying such solutions. In particular\,
we will focus on ``collapsed'' solutions and construct\, in all dimension
s $n\\ge 2$\, a large family of new examples\, including both symmetric an
d asymmetric examples\, as well as many eternal examples that do not evolv
e by translation. Moreover\, we will show that collapsed solutions decomp
ose ``backwards in time'' into a canonical configuration of Grim hyperplan
es which satisfies certain necessary conditions. This is joint work with M
at Langford and Giuseppe Tinaglia.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Schulze (University of Warwick)
DTSTART:20210921T170000Z
DTEND:20210921T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/80
DESCRIPTION:Title: Mean curvature flow with generic initial data\nby Felix Schulze (
University of Warwick) as part of Online Seminar "Geometric Analysis"\n\n\
nAbstract\nMean curvature flow is the gradient flow of the area functional
and constitutes a natural geometric heat equation on the space of hypersu
rfaces in an ambient Riemannian manifold. It is believed\, similar to Ricc
i Flow in the intrinsic setting\, to have the potential to serve as a tool
to approach several fundamental conjectures in geometry. The obstacle for
these applications is that the flow develops singularities\, which one in
general might not be able to classify completely. Nevertheless\, a well-k
nown conjecture of Huisken states that a generic mean curvature flow shoul
d have only spherical and cylindrical singularities. As a first step in th
is direction Colding-Minicozzi have shown in fundamental work that spheres
and cylinders are the only linearly stable singularity models. As a secon
d step toward Huisken's conjecture we show that mean curvature flow of gen
eric initial closed surfaces in $\\mathbb{R}^3$ avoids asymptotically coni
cal and non-spherical compact singularities. The main technical ingredient
is a long-time existence and uniqueness result for ancient mean curvature
flows that lie on one side of asymptotically conical or compact self-simi
larly shrinking solutions. This is joint work with Otis Chodosh\, Kyeongsu
Choi and Christos Mantoulidis.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Dupaigne (Université Claude Bernard Lyon 1)
DTSTART:20210928T170000Z
DTEND:20210928T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/81
DESCRIPTION:Title: The best constant in Sobolev's inequality\, joint work with Ivan Gent
il (Lyon 1) and Simon Zugmeyer (Paris 5)\nby Louis Dupaigne (Universit
é Claude Bernard Lyon 1) as part of Online Seminar "Geometric Analysis"\n
\n\nAbstract\nDue to its conformal invariance\, the sharp Sobolev inequali
ty takes\nequivalent forms on the three standard model spaces i.e. the Euc
lidean\nspace\, the round sphere and the hyperbolic space. By analogy\, we
introduce\nthree weighted manifolds named after Caffarelli\, Kohn and Nir
enberg (CKN)\nfor the following reason: the sharp Caffarelli-Kohn-Nirenber
g inequality in\nthe standard Euclidean space can be reformulated as a (sh
arp) Sobolev\ninequality written on the CKN Euclidean space. It is equival
ent to similar\n(but new) Sobolev inequalities on the CKN sphere and the C
KN hyperbolic\nspace. In addition\, the Felli-Schneider condition\, that i
s\, the region of\nparameters for which symmetry breaking occurs in the st
udy of extremals\,\nturns out to have a purely geometric interpretation as
an (integrated)\ncurvature-dimension condition. To prove these results\,
we shall use Bakry's\ngeneralization of the notion of scalar curvature\, (
a weighted version of)\nOtto's calculus\, the reformulation of all the ine
qualities (and many more)\nas entropy-entropy production inequalities alon
g appropriate gradient flows\nin Wasserstein space\, and eventually ellipt
ic PDE methods as our best tool\nfor building rigorous and concise proofs.
\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filip Rindler (University of Warwick)
DTSTART:20211005T170000Z
DTEND:20211005T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/82
DESCRIPTION:Title: Space-time integral currents of bounded variation\nby Filip Rindl
er (University of Warwick) as part of Online Seminar "Geometric Analysis"\
n\n\nAbstract\nI will present aspects of a theory of space-time integral c
urrents with bounded variation in time. This is motivated by a recent mode
l for elasto-plastic evolutions that are driven by the flow of dislocation
s (this model is joint work with T. Hudson). The classical scalar BV-theor
y can be recovered as the 0-dimensional limit case of this BV space-time t
heory. However\, the emphasis is on evolutions of higher-dimensional objec
ts\, most notably 1D loops moving within 3D domains (i.e.\, the codimensio
n 2 case)\, which corresponds to dislocation dynamics in a material specim
en. Based on this\, I will discuss the notion of Lipschitz deformation dis
tance between integral currents\, which arises physically as a (simplified
) measure of dissipation. In particular\, I will explain its relation to t
he boundaryless Whitney flat metric.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joan Verdera (Universitat Autònoma de Barcelona)
DTSTART:20211012T170000Z
DTEND:20211012T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/83
DESCRIPTION:Title: The regularity of the boundary of a vortex patch and commutators of s
ingular integrals\nby Joan Verdera (Universitat Autònoma de Barcelona
) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nI will int
roduce briefly the vorticity form of the Euler equation in the plane and s
how how singular integrals appear immediately. Then I will introduce vorte
x patches and the problem of regularity of the boundary. I will describe s
ome elements of a short proof I have found recently\, which also solves th
e regularity problem for other transport equations. Commutators of singula
r integrals play a key role\, as it is well-known.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Mondino (University of Oxford)
DTSTART:20211019T170000Z
DTEND:20211019T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/84
DESCRIPTION:Title: Optimal Transport\, weak Laplacian bounds and minimal boundaries in n
on-smooth spaces with Lower Ricci Curvature bounds\nby Andrea Mondino
(University of Oxford) as part of Online Seminar "Geometric Analysis"\n\n\
nAbstract\nThe goal of the seminar is to report on recent joint work with\
nDaniele Semola\, motivated by a question of Gromov to establish a “syn
thetic\nregularity theory" for minimal surfaces in non-smooth ambient spac
es.\n\nIn the setting of non-smooth spaces with lower Ricci Curvature boun
ds:\n\n- We establish a new principle relating lower Ricci Curvature
bounds to the\npreservation of Laplacian bounds under the evolution via t
he Hopf-Lax\nsemigroup\;
\n- We develop an intrinsic viscosity theor
y of Laplacian bounds and prove\nequivalence with other weak notions of La
placian bounds\;
\n- We prove sharp Laplacian bounds on the distance
function from a set\n(locally) minimizing the perimeter: this corresponds
to vanishing mean\ncurvature in the smooth setting\;
\n- We study t
he regularity of boundaries of sets (locally) minimizing the\nperimeter\,
obtaining sharp bounds on the Hausdorff co-dimension of the\nsingular set
plus content estimates and topological regularity of the\nregular set.
\n
\nOptimal transport plays the role of underlying technical tool fo
r addressing\nvarious points.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrik Schumacher (Chemnitz University of Technology)
DTSTART:20211026T170000Z
DTEND:20211026T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/85
DESCRIPTION:Title: Repulsive Curves and Surfaces\nby Henrik Schumacher (Chemnitz Uni
versity of Technology) as part of Online Seminar "Geometric Analysis"\n\n\
nAbstract\nRepulsive Curves and Surfaces\n\nI am going to report on recent
work on the numerical optimization of tangent-point energies of curves an
d surfaces. After a motivation and brief introduction to the central compu
tational tools (construction of suitable Riemannian metrics on the space o
f embedded manifolds\, a polyhedral discretization of the energies\, and f
ast multipole techniques)\, I am going to show a couple of numerical resul
ts. Not much about the shape of minimizers has been know so far. So\, for
the first time\, we will be able to admire the beauty of the energies' min
imizers and gradient flows.\n\nThis is based on joint work with Philipp Re
iter (Chemnitz University of Technology) and Caleb Brakensiek\, Keenan Cra
ne\, and Chris Yu (Carnegie Mellon University\, Pittsburgh).\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asaf Shachar (The Hebrew University of Jerusalem)
DTSTART:20211102T180000Z
DTEND:20211102T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/86
DESCRIPTION:Title: Non-Euclidean elasticity: Embedding surfaces with minimal distortion<
/a>\nby Asaf Shachar (The Hebrew University of Jerusalem) as part of Onlin
e Seminar "Geometric Analysis"\n\n\nAbstract\nGiven two dimensional Rieman
nian manifolds $M\,N$\, I will present a sharp lower bound on the elastic
energy (distortion) of embeddings $f:M \\to N$\, in terms of the areas' di
screpancy of $M\,N$.\n\nThe minimizing maps attaining this bound go throug
h a phase transition when the ratio of areas is $1/4$: The homotheties are
the unique energy minimizers when the ratio $\\frac{\\operatorname{Vol}(N
)}{\\operatorname{Vol}(M)} \\ge 1/4$\, and they cease being minimizers whe
n $\\frac{\\operatorname{Vol}(N)}{\\operatorname{Vol}(M)} $ gets below $1/
4$.\n\nI will describe explicit minimizers in the non-trivial regime $\\fr
ac{\\operatorname{Vol}(N)}{\\operatorname{Vol}(M)} < 1/4$ when $M\,N$ are
disks\, and give a proof sketch of the lower bound. If time permits\, I wi
ll discuss the stability of minimizers.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (University of British Columbia)
DTSTART:20211109T180000Z
DTEND:20211109T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/87
DESCRIPTION:Title: Singularity formations in some geometric flows\nby Juncheng Wei (
University of British Columbia) as part of Online Seminar "Geometric Analy
sis"\n\n\nAbstract\nI will discuss constructions of finite or infinite tim
e blow-ups for several geometric flows\, including harmonic maps flows\, h
alf-harmonic map flows and Yang-Mills flows. Phenomenon include forward
bubbling\, reverse bubbling\, bubbling continuations\, bubbling towers.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephanie Wang (UC San Diego)
DTSTART:20211116T180000Z
DTEND:20211116T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/88
DESCRIPTION:Title: Capturing surfaces with differential forms\nby Stephanie Wang (UC
San Diego) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\n
The exterior calculus of differential forms has been an important tool in
solving PDEs in geometry processing. In this talk we expand the usage of
differential forms to a whole new way of representing curves and surfaces.
By doing so we reformulate the classical nonconvex Plateau minimal surfa
ce problem into a convex optimization problem.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Schmidt
DTSTART:20220201T170000Z
DTEND:20220201T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/89
DESCRIPTION:Title: Perimeter functionals with measure datum\nby Thomas Schmidt as pa
rt of Online Seminar "Geometric Analysis"\n\n\nAbstract\nThe talk is conce
rned with perimeter functionals $\\mathscr{P}_\\mu$ given by\n\\[\n \\mat
hscr{P}_\\mu[A]:=\\mathrm{P}(A)-\\mu(A^+)\n\\]\non sets $A\\subset{\\mathb
b R}^n$ of finite volume and finite perimeter\n$\\mathrm{P}(A)$\, where th
e fixed non-negative Radon measure $\\mu$ may be\nsingular and is (necessa
rily) evaluated on a suitable closure $A^+$ of\n$A$. It will be explained
that semicontinuity and existence results for\n$\\mathscr{P}_\\mu$ crucial
ly depend on a new type of isoperimetric condition\,\nwhich also admits so
me ($n{-}1$)-dimensional measures $\\mu$\, and exemplary\nconfigurations w
ill be discussed. The long-term goal of these considerations is\nto extend
the variational approach to prescribed mean curvature hypersurfaces in\nt
he spirit of Caccioppoli\, De Giorgi\, Miranda\, Massari from $\\mathrm{L}
^1$ mean\ncurvature to mean curvature given by a possibly lower-dimensiona
l measure.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Körber (University of Vienna)
DTSTART:20211207T180000Z
DTEND:20211207T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/90
DESCRIPTION:Title: Foliations of asymptotically flat 3-manifolds by stable constant mean
curvature spheres\nby Thomas Körber (University of Vienna) as part o
f Online Seminar "Geometric Analysis"\n\n\nAbstract\nStable constant mean
curvature spheres encode important information on the asymptotic geometry
of initial data sets for isolated gravitational systems. In this talk\, I
will present a short new proof (joint with M. Eichmair) based on Lyapunov-
Schmidt reduction of the existence of an asymptotic foliation of such an i
nitial data set by stable constant mean curvature spheres. In the case whe
re the scalar curvature is non-negative\, our method also shows that the l
eaves of this foliation are the only large stable constant mean curvature
spheres that enclose the center of the initial data set.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josef Bemelmans (RWTH Aachen University)
DTSTART:20211214T180000Z
DTEND:20211214T190000Z
DTSTAMP:20260404T110912Z
UID:OSGA/91
DESCRIPTION:Title: A Central Result from Newton's Principia Mathematica: The Body of Lea
st Resistance\nby Josef Bemelmans (RWTH Aachen University) as part of
Online Seminar "Geometric Analysis"\n\n\nAbstract\nIn Newton's Principia M
athematica fundamental theorems\, e.g about the motion of planets around t
he sun\, are proven by methods of ancient geometry rather than infinitesim
al analysis\, as one might expect. There are however problems in the Princ
ipia that are treated using techniques from calculus\; we present one that
in today's terminology belongs to the calculus of variations: to determin
e the shape of a rotationally symmetric body of prescribed base and height
such that its resistance in a uniform fluid flow becomes minimal.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmichele Di Matteo (Karlsruhe Institute of Technology)
DTSTART:20220111T170000Z
DTEND:20220111T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/92
DESCRIPTION:Title: A Local Singularity Analysis for the Ricci flow\nby Gianmichele D
i Matteo (Karlsruhe Institute of Technology) as part of Online Seminar "Ge
ometric Analysis"\n\n\nAbstract\nIn this talk\, I will describe a refined
local singularity analysis for the Ricci flow developed jointly with R. Bu
zano. The key idea is to investigate blow-up rates of the curvature tensor
locally\, near a singular point. Then I will show applications of this th
eory to Ricci flows with scalar curvature bounded up to the singular time.
\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leah Schätzler (University Salzburg)
DTSTART:20220118T170000Z
DTEND:20220118T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/93
DESCRIPTION:Title: Hölder continuity for a doubly nonlinear equation\nby Leah Schä
tzler (University Salzburg) as part of Online Seminar "Geometric Analysis"
\n\n\nAbstract\nThe prototype of the partial differential equations consid
ered in this talk is\n$$\n\\partial_t \\big( |u|^{q-1} u \\big) - \\operat
orname{div} \\big( |Du|^{p-2} Du \\big) = 0\n\\quad \\text{in } E_T = E \\
times (0\,T] \\subset \\mathbb{R}^{N+1}\n$$\nwith parameters $q>0$ and $p>
1$.\nWell-known special cases of this doubly nonlinear equation are the po
rous medium equation ($p=2$)\, the parabolic $p$-Laplace equation ($q=1$)
and Trudinger's equation ($q=p-1$).\nI will present H\\"older continuity r
esults based on joint work with Verena B\\"ogelein\, Frank Duzaar and Naia
n Liao.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Stanin (University Salzburg)
DTSTART:20220125T170000Z
DTEND:20220125T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/94
DESCRIPTION:Title: Global continuity of variational solutions weakening the one-sided bo
unded slope condition\nby Thomas Stanin (University Salzburg) as part
of Online Seminar "Geometric Analysis"\n\n\nAbstract\nIn this talk\, we ha
ve a look at regularity properties of variational solutions to a class of
Cauchy-Dirichlet problems of the form\n\n$$\n\\begin{cases}\n\\partial_t u
- \\mathrm{div}_x (D_\\xi f(Du)) = 0 & \\text{in}\\ \\Omega_T\, \\\\\nu =
u_0 & \\text{on}\\ \\partial_\\mathcal{P}\\Omega_T.\n\\end{cases}\n$$\n\n
We do not impose any growth conditions from above on $f \\colon \\R^n \\to
\\R$ but require it to be convex and coercive. The domain $\\Omega \\subs
et \\R^n$ is supposed to be bounded and convex and for the time-independen
t boundary datum $u_0 \\colon \\overline\\Omega \\to \\R$\, we require con
tinuity. These assumptions on $u_0$ are weaker than a one-sided version of
the bounded slope condition. We present a result showing variational solu
tions $u \\colon \\Omega_T \\to \\R$ to these problem class to be globally
continuous.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandra Pluda (University of Pisa)
DTSTART:20220208T170000Z
DTEND:20220208T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/95
DESCRIPTION:Title: Resolution of singularities of the network flow\nby Alessandra Pl
uda (University of Pisa) as part of Online Seminar "Geometric Analysis"\n\
n\nAbstract\nThe curve shortening flow is an evolution equation in which a
curve moves with normal velocity equal to its curvature (at any point and
time) and can be interpreted as the gradient flow of the length. We consi
der the same flow for networks (finite unions of sufficiently smooth\ncurv
es whose end points meet at junctions). Because of the variational nature
of the problem\, one expects that for almost all the times the evolving ne
twork will possess only triple junctions where the unit tangent vectors fo
rms angles of 120 degrees (regular junctions). However\, even if the initi
al network has only regular junctions\, this property is not preserved by
the flow and junctions of four or more curves may appear during the evolut
ion.\nThe aim of this talk is first to describe the process of singularity
formation and then\nto explain the resolution of such singularities and h
ow to continue the flow in a classical PDE framework.\n\nThis is a researc
h in collaboration with Jorge Lira (Universidade Federal do Ceará)\, \nR
afe Mazzeo (Stanford University) and Mariel Saez (P. Universidad Catolic
a de Chile).\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyron Vellis (University of Tennessee\, Knoxville)
DTSTART:20220215T170000Z
DTEND:20220215T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/96
DESCRIPTION:Title: Bi-Lipschitz embeddings\nby Vyron Vellis (University of Tennessee
\, Knoxville) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract
\nTo improve our understanding of a metric space\, it is often\nhelpful to
realize the space within some Euclidean space. The embedding\nproblem is
concerned with recognizing those spaces which admit an embedding\ninto som
e Euclidean space that does not distort its geometry too much. The\nbi-Lip
schitz emebedding problem is concerned with identifying those metric\nspac
es for which such an embedding exists. The embedding problem has\nrecently
generated great interest in theoretical computer science and\, more\nspec
ifically\, in graphic imaging and storage and access issues for large\ndat
a sets. In the first part of the talk we will examine the embeddability\no
f two well-known sub-Riemannian manifolds\, the Grushin plane and the\nHei
senberg group. In the second part we will discuss the embeddability of\nme
tric trees with good geometry. The talk is based on joint works with\nRomn
ey (2017)\, Li\, Chousionis\, and Zimmerman (2020)\, David (2020)\, and Da
vid\nand Eriksson-Bique (2021).\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azahara DelaTorre (Sapienza Università di Roma)
DTSTART:20220222T170000Z
DTEND:20220222T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/97
DESCRIPTION:Title: The fractional Yamabe problem with singularities\nby Azahara Dela
Torre (Sapienza Università di Roma) as part of Online Seminar "Geometric
Analysis"\n\n\nAbstract\nThe so called Yamabe problem in Conformal Geometr
y consists in finding a metric conformal to a given one and which has cons
tant scalar curvature. From the analytic point of view\, this problem beco
mes a semilinear elliptic PDE with critical (for the Sobolev embedding) po
wer non-linearity. If we study the problem in the Euclidean space\, allowi
ng the presence of nonzero-dimensional singularities can be transformed in
to reducing the non-linearity to a Sobolev-subcritical power. A quite rece
nt notion of non-local curvature gives rise to a parallel study which weak
ens the geometric assumptions giving rise to a non-local semilinear ellipt
ic PDE. \n\nIn this talk\, we will focus on metrics which are singular alo
ng nonzero-dimensional singularities. In collaboration with Ao\, Chan\, Fo
ntelos\, González and Wei\, we covered the construction of solutions whic
h are singular along (zero and positive dimensional) smooth submanifolds i
n this fractional setting. This was done through the development of new me
thods coming from conformal geometry and Scattering theory for the study o
f non-local ODEs. Due to the limitations of the techniques we used\, the p
articular case of ``maximal’’ dimension for the singularity was not co
vered. In a recent work\, in collaboration with H. Chan\, we cover this sp
ecific dimension constructing and studying singular solutions of critical
dimension.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Adamowicz (Polish Academy of Sciences in Warsaw)
DTSTART:20220301T170000Z
DTEND:20220301T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/98
DESCRIPTION:Title: Isoperimetric inequalities and curvature of level sets for harmonic f
unctions on smooth and singular surfaces\nby Tomasz Adamowicz (Polish
Academy of Sciences in Warsaw) as part of Online Seminar "Geometric Analys
is"\n\n\nAbstract\nOne of the main themes of the talk are monotonicity for
mulas for\nlevel sets of harmonic functions in Euclidean domains and Riema
nnian\nsurfaces\, including the singular Alexandrov surfaces. Such formula
s allow\nfor studying the logarithmic convexity of the length of the level
curves and\nrelated isoperimetric type inequalities. Related are the stud
ies of the\ngeodesic curvature of the level curves and of the steepest des
cent.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohameden Ahmedou (Universitty of Giessen)
DTSTART:20220308T170000Z
DTEND:20220308T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/99
DESCRIPTION:Title: New Blow up phenomena for the Nirenberg's problem on half spheres
\nby Mohameden Ahmedou (Universitty of Giessen) as part of Online Seminar
"Geometric Analysis"\n\n\nAbstract\nIn this talk I will report on a refi
ned blow up analysis of finite energy approximated solutions to the Niren
berg's problem on half spheres. The later consists of prescribing under
minimal boundary conditions the scalar curvature to be a given function. I
n particular we give a precise location of blow up points and blow up rate
s. Such an analysis shows that the blow up picture of the Nirenberg's prob
lem on half spheres is far more complicated that in the case of closed sph
eres. Indeed besides the combination of interior and boundary blow ups\, t
here are "non simples blow ups" for subcritical solutions having zero or
nonzero weak limit. The formation of such non simple blow ups is govern
ed by a vortex problem\, unveiling an unexpected connection with Euler e
quations in fluid dynamic and mean fields type equations in mathematical p
hysics.\nThis is joint work with Mohamed Ben Ayed (Sfax University).\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Young (New York University)
DTSTART:20220322T170000Z
DTEND:20220322T180000Z
DTSTAMP:20260404T110912Z
UID:OSGA/101
DESCRIPTION:Title: Metric differentiation and embeddings of the Heisenberg group\nb
y Robert Young (New York University) as part of Online Seminar "Geometric
Analysis"\n\n\nAbstract\nThe Heisenberg group is the simplest example of a
noncommutative nilpotent Lie group. In this talk\, we will explore how th
at noncommutativity affects geometry and analysis in the Heisenberg group.
We will describe why good embeddings of $\\mathbb{H}$ must be bumpy at ma
ny scales\, how to study embeddings into $L_1$ by studying surfaces in $\\
mathbb{H}$\, and how to construct a metric space which embeds into $L_1$ a
nd $L_4$ but not in $L_2$. This talk is joint work with Assaf Naor.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria G. Westdickenberg (RWTH Aachen University)
DTSTART:20220426T160000Z
DTEND:20220426T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/103
DESCRIPTION:Title: Convergence and metastability of (weakly) nonconvex gradient flows\nby Maria G. Westdickenberg (RWTH Aachen University) as part of Online
Seminar "Geometric Analysis"\n\n\nAbstract\nTogether with Felix Otto\, Ric
hard Schubert\, and other collaborators\, we have\ndeveloped two different
energy-based methods to capture convergence and metastability. We have\nu
sed these methods to establish optimal\, algebraic convergence for the Mul
lins-Sekerka (MS)\nproblem in the plane and the Cahn-Hilliard equation on
the line. After a general introduction of the central ideas\, we comment i
n particular on the role of curvature in the MS problem. Work in progress
with Richard Schubert and Felix Otto extends the L1-based method to the Mu
llins-Sekerka evolution in three dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Gerhards (TU Freiberg)
DTSTART:20220329T160000Z
DTEND:20220329T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/104
DESCRIPTION:Title: Some inverse magnetization problems motivated from geoscience\nb
y Christian Gerhards (TU Freiberg) as part of Online Seminar "Geometric An
alysis"\n\n\nAbstract\nWe present an overview on some aspects of geomagnet
ic inverse problems related to Hardy spaces on the sphere/Lipschitz surfac
es\, Helmholtz Hodge decomposition on Lipschitz domains\, and spatial loca
lization. A particular focus is on uniqueness issues and the influence of
discretization (e.g.\, if the geometry of the discretization influences un
iqueness). The talk will on the on hand try to motivate the geophysical ba
ckground of these problems and provide some basic examples\, and on the ot
her hand present a proper analysis of the problems.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michał Miśkiewicz (Institute of Mathematics\, Polish Academy of
Sciences)
DTSTART:20220405T160000Z
DTEND:20220405T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/105
DESCRIPTION:Title: Struggles with the regularity of $n$-harmonic maps\nby Michał M
iśkiewicz (Institute of Mathematics\, Polish Academy of Sciences) as part
of Online Seminar "Geometric Analysis"\n\n\nAbstract\nLet us consider the
Dirichlet $n$-energy $\\int_{\\mathcal{M}} |\\nabla u|^n$ for maps $u \\c
olon \\mathcal{M}^n \\to \\mathcal{N}^m$ between two Riemannian manifolds.
Its Euler-Lagrange system – known as the $n$-harmonic equation – is a
n example of a conformally invariant system with critical nonlinearity. In
general such systems can have discontinuous solutions\, but the regularit
y of $n$-harmonic maps is an open problem for $n > 2$. \n\nPartial results
in this direction rely on the jacobian structure of the $n$-harmonic equa
tion\, together with the theory of Hardy and BMO spaces. After a brief rev
iew of these methods\, I will describe a new application\, which leads to
yet another partial result – regularity for $W^{n/2\,2}$-solutions – b
ut also gives some hope for further progress. \n\nThis is joint work with
Paweł Strzelecki and Bogdan Petraszczuk.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Chen (Georg-August-Universität Göttingen)
DTSTART:20220412T160000Z
DTEND:20220412T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/106
DESCRIPTION:Title: Gluing constructions of minimal surfaces: Recent progress and future
plans\nby Hao Chen (Georg-August-Universität Göttingen) as part of
Online Seminar "Geometric Analysis"\n\n\nAbstract\nI will review our recen
t constructions of minimal surfaces by gluing catenoids\, helicoids\, and
saddle towers. In particular\, we recently resolved some technical issues
in previous similar constructions and revealed surprising connections bet
ween minimal surfaces and fluid dynamics. Moreover\, I will discuss possi
bilities of further improving the gluing techniques. The talk covers join
t works with Martin Traizet and Daniel Freese.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jasmin Hörter (Karlsruhe Institut of Technology)
DTSTART:20220802T160000Z
DTEND:20220802T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/107
DESCRIPTION:Title: Rigidity of $\\epsilon$-harmonic maps of low degree\nby Jasmin H
örter (Karlsruhe Institut of Technology) as part of Online Seminar "Geome
tric Analysis"\n\n\nAbstract\nIn 1981 Sacks and Uhlenbeck introduced their
famous alpha-approximation of the Dirichlet energy for maps from surfaces
and showed that critical points converge (away from finitely many points)
to a harmonic map. Now one can ask whether every harmonic map is captured
by this limiting process. Lamm\, Malchiodi and Micallef answered this for
maps from the two sphere into the two sphere and showed that the Sacks-Uh
lenbeck method produces only constant maps and rotations if the energy lie
s below a certain threshold. We investigate the same question for the epsi
lon-approximation of the Dirichlet energy.\nJoint work with Tobias Lamm an
d Mario Micallef.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sara Daneri (Gran Sasso Science Institute)
DTSTART:20220927T160000Z
DTEND:20220927T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/108
DESCRIPTION:Title: Symmetry breaking and pattern formation for functionals with competi
ng interactions\nby Sara Daneri (Gran Sasso Science Institute) as part
of Online Seminar "Geometric Analysis"\n\n\nAbstract\nIn this talk we wil
l review some recent results we obtained on the one-dimensionality of the
minimizers\nof a family of continuous local/nonlocal interaction functiona
ls in general dimension. Such functionals have a local term\, typically th
e perimeter or its Modica-Mortola approximation\, which penalizes interfac
es\, and a nonlocal term favouring oscillations which are high in frequenc
y and in amplitude. The competition between the two terms is expected by e
xperiments and simulations to give rise to periodic patterns at equilibriu
m. Functionals of this type are used to model pattern formation\, either
in material science or in biology. The difficulty in proving the emergenc
e of such structures is due to the fact that the functionals are symmetric
with respect to permutation of coordinates\, while in more than one space
dimensions minimizers are one-dimensional\, thus losing the symmetry prop
erty of the functionals. We will present new techniques and results showin
g that for two classes of functionals (used to model generalized anti-ferr
omagnetic systems\, respectively colloidal suspensions)\, both in sharp
interface and in diffuse interface models\, minimizers are one-dimensional
and periodic\, in general dimension and also while imposing a nontrivial
volume constraint. The results are contained in a series of joint works wi
th Eris Runa and Alicja Kerschbaum.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Lagemann (RWTH Aachen University)
DTSTART:20220503T160000Z
DTEND:20220503T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/109
DESCRIPTION:Title: Tangent-point energies as Gamma-limit of discrete tangent-point ener
gies on biarc curves\nby Anna Lagemann (RWTH Aachen University) as par
t of Online Seminar "Geometric Analysis"\n\n\nAbstract\nUsing interpolatio
n with biarc curves we prove $\\Gamma$-convergence of discretized tangent-
point energies to the continuous tangent-point energies in the $C^1$-topol
ogy. As a consequence\, discrete almost minimizing biarc curves converge t
o minimizers of the continuous tangent-point energies. In addition\, takin
g point-tangent data from a given $C^{1\,1}$-curve $\\gamma$\, we establis
h convergence of the discrete energies evaluated on biarc curves interpola
ting these data\, to the continuous tangent-point energy of $\\gamma$\, to
gether with an explicit convergence rate. This is joint work with Heiko vo
n der Mosel.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gael Yomgne Diebou (Uni Bonn)
DTSTART:20220510T160000Z
DTEND:20220510T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/110
DESCRIPTION:Title: Well-posedness theory for the weakly harmonic maps problem subject t
o irregular data\nby Gael Yomgne Diebou (Uni Bonn) as part of Online S
eminar "Geometric Analysis"\n\n\nAbstract\nWe study the existence\, unique
ness and regularity of weakly harmonic maps\ninto a closed Riemannian mani
fold. In this talk\, I will emphasize on the\nnovel ideas\, based on intri
nsic features of the problem and modern\nharmonic analysis tools which all
ow us to prescribe Dirichlet data with\ninfinite energy. More precisely\,
we prove that under a mere smallness\nhypothesis on the boundary data meas
ured in the $L^{\\infty}$ or $BMO$\nnorm\, there exists a unique solution
which is locally infinitely smooth.\nWhile this regularity feature fails i
n absence of the smallness assumption\,\nexistence still persists for larg
e data provided the domain is bounded and\nthere exist smooth stable weak
ly harmonic maps.\nThis is a joint work with Herbert Koch.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Hyder (TIFR-CAM\, Bangalore)
DTSTART:20220524T160000Z
DTEND:20220524T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/111
DESCRIPTION:Title: Blow-up analysis and partial regularity results for Liouville type e
quations\nby Ali Hyder (TIFR-CAM\, Bangalore) as part of Online Semina
r "Geometric Analysis"\n\n\nAbstract\nDue to the presence of the exponenti
al nonlinearity\, the Liouville equation in dimension three and higher is
supercritical. In particular\, it admits several singular solutions. We wi
ll talk about asymptotic behavior of a family of stationary solutions\, an
d how to use it to obtain partial regularity results.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannes Matt (RWTH Aachen University)
DTSTART:20220531T160000Z
DTEND:20220531T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/113
DESCRIPTION:Title: Banach gradient flows for various families of knot energies\nby
Hannes Matt (RWTH Aachen University) as part of Online Seminar "Geometric
Analysis"\n\n\nAbstract\nThis is joint work with Daniel Steenebrügge and
Heiko von der Mosel. We establish long-time existence of Banach gradient f
lows for generalised integral Menger curvatures and tangent-point energies
\, and for O'Hara's self-repulsive potentials $E^{\\alpha\,p}$. In order t
o do so\, we employ the theory of curves of maximal slope in slightly smal
ler spaces compactly embedding into the respective energy spaces associate
d to these functionals\, and add a term involving the logarithmic strain\,
which controls the parametrisations of the flowing (knotted) loops. As a
prerequisite\, we prove in addition that O'Hara's knot energies $E^{\\alph
a\,p}$ are continuously differentiable.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Laux (University of Bonn)
DTSTART:20220621T160000Z
DTEND:20220621T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/114
DESCRIPTION:Title: Local minimizers of the area functional based on a concept of local
paired calibrations\nby Tim Laux (University of Bonn) as part of Onlin
e Seminar "Geometric Analysis"\n\n\nAbstract\nCalibrations are an elegant
tool to prove that a given surface (or surface cluster) minimizes the area
functional. In this talk\, I will present a way to extend the notion of (
paired) calibrations to the setting when one can only hope for local minim
ality. Based on this notion\, one can show that any partition of the plane
\, whose network of interfaces consists of finitely many straight segments
with a singular set made up of finitely many triple junctions at which th
e Herring angle condition is satisfied\, is a local minimizer of the inter
face energy with respect to $L^1$ perturbations of the phases. This result
not only holds for the case of the area functional but for a general clas
s of surface tension matrices.\n\nThis is based on joint work with Julian
Fischer\, Sebastian Hensel\, and Theresa Simon.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Bortz (University of Alabama)
DTSTART:20220614T160000Z
DTEND:20220614T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/115
DESCRIPTION:Title: Caloric Measure and Parabolic Uniform Rectifiability\nby Simon B
ortz (University of Alabama) as part of Online Seminar "Geometric Analysis
"\n\n\nAbstract\nIn the late 70's Dahlberg showed that harmonic measure an
d surface measure are mutually absolutely continuous in Lipschitz domains
in $\\mathbb{R}^d$ (this was a long standing conjecture). In fact\, he sho
wed a stronger quantitative version of mutual absolute continuity \, $A_\\
infty$\, which is equivalent to certain $L^p$ estimates on solutions. It w
as conjectured by Hunt that the same is true in the parabolic setting\, th
at is\, for parabolic Lipschitz graph domains\; however\, this turned out
to be false as a counterexample was produced by Kaufman and Wu. On the oth
er hand\, it was later shown by Lewis and Murray that if the graphs had a
little more time-regularity then Dahlberg's theorem holds.\n\nTogether wit
h my co-authors\, we have shown the work of Lewis and Murray is sharp. In
particular\, if a domain is given by the region above a parabolic Lipschit
z graph the $A_\\infty$ property of caloric measure is equivalent to this
extra time regularity. These `regular' parabolic Lipschitz graphs are the
prototypical parabolic uniformly rectifiable (P-UR) sets and this project
is part of a larger program to characterize P-UR sets by properties of cal
oric functions/measure.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Augusto Ponce (Université catholique de Louvain)
DTSTART:20220628T160000Z
DTEND:20220628T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/116
DESCRIPTION:Title: A topological toolbox for Sobolev maps\nby Augusto Ponce (Univer
sité catholique de Louvain) as part of Online Seminar "Geometric Analysis
"\n\n\nAbstract\nClassical works by F. Bethuel and by F. Hang and F-H. Lin
have\nidentified the local and global topological obstructions that preve
nt smooth\nmaps from being dense in the Sobolev space \\(W^{1\, p}(M^{m}\;
N^{n})\\)\nbetween two Riemannian manifolds when \\(p < m\\). They are re
lated to the\nextension of continuous maps from subsets of \\(M^{m}\\) to
\\(N^{n}\\).\n\nIn this talk I will present some work in progress with P.
Bousquet\n(Toulouse) and J. Van Schaftingen (UCLouvain)\, inspired from th
e notions of\nmodulus introduced by B. Fuglede and degree for VMO maps by
H. Brezis and L.\nNirenberg.\nI shall explain how one can decide whether a
specific Sobolev map \\(u :\nM^{m} \\to N^{n}\\) can be approximated or n
ot by smooth ones\, even in the\npresence of topological obstructions from
\\(M^{m}\\) or \\(N^{n}\\).\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Tolsa (ICREA - Universitat Autònoma de Barcelona - CRM)
DTSTART:20220705T160000Z
DTEND:20220705T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/117
DESCRIPTION:Title: The regularity problem for the Laplace equation and boundary Poincar
é inequalities in rough domains\nby Xavier Tolsa (ICREA - Universitat
Autònoma de Barcelona - CRM) as part of Online Seminar "Geometric Analys
is"\n\n\nAbstract\nGiven a bounded domain $\\Omega \\subset \\mathbb R^n$\
, one says that the\n$L^p$-regularity problem is solvable for the Laplace
equation in $\\Omega$\nif\, given any continuous function $f$ defined in $
\\partial \\Omega$ and the\nharmonic extension $u$ of $f$ to $\\Omega$\, t
he non-tangential maximal\nfunction of the gradient of $u$ can be controll
ed in $L^p$ norm by the\ntangential derivative of $f$ in $\\partial\\Omega
$. Up to quite recently this\nwas only known to hold for Lipschitz domains
(in some range of $p$'s). \nIn my talk I will explain a recent result wit
h Mihalis Mourgoglou where we\nshow that the $L^p$-regularity is also solv
able in more general domains\,\nsuch as 2-sided chord-arc domains. In the
solution of this problem\, the\nPoincaré inequality in the boundary of th
e domain plays an important role. I\nwill also discuss this issue and a re
lated joint result with Olli Tapiola\nwhere we show that the boundaries of
2-sided chord-arc domains support\n1-Poincaré inequalities.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guozhen Lu (University of Connecticut)
DTSTART:20220920T160000Z
DTEND:20220920T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/118
DESCRIPTION:Title: Helgason-Fourier analysis techniques in sharp geometric inequalities
on hyperbolic spaces\nby Guozhen Lu (University of Connecticut) as pa
rt of Online Seminar "Geometric Analysis"\n\n\nAbstract\nIn recent years\,
we have developed a new approach to establish sharp geometric and functio
nal inequalities using the Helgason-Fourier analysis techniques on symmetr
ic spaces. Such inequalities include sharp higher order Hardy-Sobolev-Maz'
ya and Hardy-Adams inequalities on hyperbolic spaces on all Riemannian sym
metric spaces of noncompact type of rank one. Precise expressions of Green
's functions of GJMS operators on real hyperbolic spaces in terms of hyper
geometric functions are established as well.This is based on a series of j
oint works with Joshua Flynn\, Jungang Li\, and Qiaohua Yang.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Goering
DTSTART:20220719T160000Z
DTEND:20220719T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/119
DESCRIPTION:Title: Finslerian regularity theory in Euclidean space\nby Max Goering
as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nIn the setti
ng of sets of finite perimeter\, the regularity of\nsurfaces minimizing $\
\| \\cdot \\|_{p}$-surface energies is entirely unknown.\nSince these ener
gies do not satisfy Almgren's ellipticity condition\, the PDE\nthat arises
(as the partial linearization in the small gradient regime of\nthe anisot
ropic minimal surface) is very degenerate elliptic. In this\nexample\, the
relevant PDE is the Finsler $\\gamma$-Laplacian. This motivates\na discus
sion of the state-of-the-art regularity theory for the very\ndegenerate el
liptic and non-linear Finsler $\\gamma$-Laplacian. Pending time\,\nsome po
tential applications to classical questions in geometric measure\ntheory w
ill also be discussed. This talk discusses joint work.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Menne (National Taiwan Normal University and National Cente
r for Theoretical Sciences)
DTSTART:20220726T160000Z
DTEND:20220726T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/120
DESCRIPTION:Title: Integral chains with coefficients in a complete normed commutative g
roup\nby Ulrich Menne (National Taiwan Normal University and National
Center for Theoretical Sciences) as part of Online Seminar "Geometric Anal
ysis"\n\n\nAbstract\nAs a service to the community\, in joint work with Ch
ristian Scharrer\, we provide—for Euclidean space—a basic treatment of
locally rectifiable chains and of the complex of locally integral chains.
In this setting\, we may beneficially develop the idea of a complete norm
ed commutative group bundle over the Grassmann manifold whose fibre is the
coefficient group of the chains. Our exposition also sheds new light on s
ome algebraic aspects of the theory. Finally\, we indicate an extension to
a geometric approach to locally flat chains centring on locally rectifiab
le chains rather than completion procedures.\n\nThe virtual whiteboard https://mi
ro.com/app/board/uXjVOpucY68=/ will be employed\; its password protect
ion will be removed for the duration of the presentation. There will be n
o recording for this talk.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannick Sire (Johns Hopkins University)
DTSTART:20220913T160000Z
DTEND:20220913T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/121
DESCRIPTION:Title: Harmonic maps with free boundary and beyond\nby Yannick Sire (Jo
hns Hopkins University) as part of Online Seminar "Geometric Analysis"\n\n
\nAbstract\nI will introduce a new heat flow for harmonic maps with free b
oundary. After giving some motivations to study such maps in relation with
extremal metrics in spectral geometry\, I will construct weak solutions f
or the flow and derive their partial regularity. The introduction of this
new flow is motivated by the so-called half-harmonic maps introduced by Da
Lio and Riviere\, which provide a new approach to the old topic of harmon
ic maps with free boundary. I will also state some open problems and possi
ble generalizations.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Fischer (IST Austria)
DTSTART:20220906T160000Z
DTEND:20220906T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/122
DESCRIPTION:Title: Multiphase Mean Curvature Flow: Uniqueness Properties of Weak Soluti
on Concepts and Phase-Field Approximations\nby Julian Fischer (IST Aus
tria) as part of Online Seminar "Geometric Analysis"\n\n\nAbstract\nTopolo
gy changes occur naturally in geometric evolution equations like mean curv
ature flow. As classical solution concepts break down at such geometric si
ngularities\, the use of weak solution concepts becomes necessary in order
to describe topological changes. For two-phase mean curvature flow\, the
theory of viscosity solutions by Chen-Giga-Goto and Evans-Spruck provides
a concept of weak solutions with basically optimal existence and uniquenes
s properties. In contrast\, the uniqueness properties of weak solution con
cepts for multiphase mean curvature flow had remained mostly unexplored.\n
\nBy introducing a novel concept of "gradient flow calibrations"\, we esta
blish a weak-strong uniqueness principle for multiphase mean curvature flo
w: Weak (BV) solutions to multiphase mean curvature flow are unique as lon
g as a classical solution exists. In particular\, in planar multiphase mea
n curvature flow\, weak (BV) solutions are unique prior to the first topol
ogical change. As basic counterexamples show\, the uniqueness of evolution
s may fail past certain topology changes\, demonstrating the optimality of
our result.\n\nIn the last part of the talk\, we discuss further applicat
ions of our new concept\, including the quantitative convergence of diffus
e-interface (Allen-Cahn) approximations for multiphase mean curvature flow
.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Brazke (University of Heidelberg)
DTSTART:20221011T160000Z
DTEND:20221011T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/126
DESCRIPTION:Title: Γ–limit for a sharp interface model related to pattern formation
on biomembranes\nby Denis Brazke (University of Heidelberg) as part of
Online Seminar "Geometric Analysis"\n\n\nAbstract\nWe derive a macroscopi
c limit for a sharp interface version of a model proposed by Komura\, Shim
okawa and Andelman to investigate pattern formation in biomembranes due to
competition of chemical and mechanical forces. We identify sub- and super
crital parameter regimes and show with the introduction of the autocorrela
tion function that the ground state energy leads to the isoperimetric prob
lem in the subcritical regime\, which is interpreted to not form fine scal
e patterns\n\nThis is joint work with Hans Knüpfer and Anna Marciniak--Cz
ochra.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ernst Kuwert (University of Freiburg i. Br.)
DTSTART:20221018T160000Z
DTEND:20221018T170000Z
DTSTAMP:20260404T110912Z
UID:OSGA/127
DESCRIPTION:Title: Curvature varifolds with orthogonal boundary\nby Ernst Kuwert (U
niversity of Freiburg i. Br.) as part of Online Seminar "Geometric Analysi
s"\n\n\nAbstract\nThe talk is concerned with the existence of upper mass b
ounds for $m$-dimensional surfaces in terms of curvature integrals. We foc
us on the case of surfaces confined to a set $\\Omega$ in ${\\mathbb R}^n$
meeting $\\partial \\Omega$ orthogonally along their boundary (joint work
with Marius Müller\, Freiburg). In a previous paper with Victor Bangert
(Freiburg) there is a related result for $2$-dimensional surfaces in Riema
nnian manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/OSGA/127/
END:VEVENT
END:VCALENDAR