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SUMMARY:Theodora Bourni (University of Tennessee Knoxville)
DTSTART:20210504T143000Z
DTEND:20210504T153000Z
DTSTAMP:20260404T111103Z
UID:GALSeminar/1
DESCRIPTION:Title: Ancient solutions to mean curvature flow\nby Theodora Bourni
(University of Tennessee Knoxville) as part of Geometric Analysis in the
Large\n\n\nAbstract\nMean curvature flow (MCF) is the gradient flow of the
area functional\; it moves the surface in the direction of steepest decre
ase of area. An important motivation for the study of MCF comes from its
potential geometric applications\, such as classification theorems and geo
metric inequalities. MCF develops “singularities” (curvature blow-up)\
, which obstruct the flow from existing for all times and therefore unders
tanding these high curvature regions is of great interest. This is done b
y studying ancient solutions\, solutions that have existed for all times i
n the past\, and which model singularities. In this talk we will discuss t
heir importance and ways of constructing and classifying such solutions. I
n particular\, we will focus on “collapsed” solutions and construct\,
in all dimensions n>=2\, a large family of new examples\, including both s
ymmetric and asymmetric examples\, as well as many eternal examples that d
o not evolve by translation. Moreover\, we will show that collapsed solut
ions decompose “backwards in time” into a canonical configuration of G
rim hyperplanes which satisfies certain necessary conditions. This is join
t work with Mat Langford and Giuseppe Tinaglia.\n
LOCATION:https://stable.researchseminars.org/talk/GALSeminar/1/
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SUMMARY:Barbara Nelli (Università dell’Aquila)
DTSTART:20210511T143000Z
DTEND:20210511T153000Z
DTSTAMP:20260404T111103Z
UID:GALSeminar/2
DESCRIPTION:Title: Hypersurfaces with constant higher order mean curvature\nby
Barbara Nelli (Università dell’Aquila) as part of Geometric Analysis in
the Large\n\n\nAbstract\nWe give an overview of some old and new results
about the shape of hypersurfaces whose one of the symmetric functions of t
he principal curvature is constant.\n
LOCATION:https://stable.researchseminars.org/talk/GALSeminar/2/
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SUMMARY:Laurent Mazet (Université de Tours)
DTSTART:20210518T143000Z
DTEND:20210518T153000Z
DTSTAMP:20260404T111103Z
UID:GALSeminar/3
DESCRIPTION:Title: Rigidity of Riemannian manifolds containing an equator\nby L
aurent Mazet (Université de Tours) as part of Geometric Analysis in the L
arge\n\n\nAbstract\nIf a Riemannian sphere S^2 with curvature between 0 an
d 1 has a closed geodesic of length 2\\pi\, then its curvature is constant
and equal to 1. This result is due to Calabi. In dimension 3 and under th
e same curvature assumptions\, the existence of a minimal sphere of area 4
\\pi rigidifies the metric. This result has been obtained in a preceding w
ork with H. Rosenberg. In this talk\, I will explain how this work can be
generalized in higher dimension. As a consequence\, I will also give a rig
idity result concerning Simon-Smith width.\n
LOCATION:https://stable.researchseminars.org/talk/GALSeminar/3/
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SUMMARY:Ezequiel Barbosa (Universidad de Granada / Universidade Federal de
Minas Gerais)
DTSTART:20210525T143000Z
DTEND:20210525T153000Z
DTSTAMP:20260404T111103Z
UID:GALSeminar/4
DESCRIPTION:Title: Some characterization results of the Delaunay Surfaces\nby E
zequiel Barbosa (Universidad de Granada / Universidade Federal de Minas Ge
rais) as part of Geometric Analysis in the Large\n\n\nAbstract\nIn this ta
lk we will discuss some new characterization results of some Delaunay capi
llary surfaces in a Euclidean ball.\n
LOCATION:https://stable.researchseminars.org/talk/GALSeminar/4/
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SUMMARY:Marco Guaraco (Imperial College London)
DTSTART:20210601T143000Z
DTEND:20210601T153000Z
DTSTAMP:20260404T111103Z
UID:GALSeminar/5
DESCRIPTION:Title: Mean curvature flow in homology and foliations of hyperbolic 3-m
anifolds\nby Marco Guaraco (Imperial College London) as part of Geomet
ric Analysis in the Large\n\n\nAbstract\nWe will discuss global aspects an
d applications of the mean curvature flow and min-max in closed manifolds.
Topics include: non-separating hypersurfaces with non-vanishing mean curv
ature\, incompressible surfaces\, existence of monotone isotopies towards
stable minimal surfaces\, foliations of hyperbolic 3-manifolds and outermo
st minimal surfaces in quasi-Fuchsian ends. This is a joint work with Vand
erson Lima and Franco Vargas Pallete.\n
LOCATION:https://stable.researchseminars.org/talk/GALSeminar/5/
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SUMMARY:José Espinar (Universidad de Cádiz)
DTSTART:20210608T143000Z
DTEND:20210608T153000Z
DTSTAMP:20260404T111103Z
UID:GALSeminar/6
DESCRIPTION:Title: On non-compact free boundary minimal hypersurfaces in the Rieman
nian Schwarzschild spaces\nby José Espinar (Universidad de Cádiz) as
part of Geometric Analysis in the Large\n\n\nAbstract\nWe will show that\
, in contrast with the 3-dimensional case\, the Morse index of a free boun
dary rotationally symmetric totally geodesic hypersurface of the n-dimensi
onal Riemannnian Schwarzschild space with respect to variations that are t
angential along the horizon is zero\, for n≥4. Moreover\, we will show t
hat there exist non-compact free boundary minimal hypersurfaces which are
not totally geodesic\, n≥8\, with Morse index equal to zero. Also\, for
n≥4\, there exist infinitely many non-compact free boundary minimal hype
rsurfaces\, which are not congruent to each other\, with infinite Morse in
dex.\n
LOCATION:https://stable.researchseminars.org/talk/GALSeminar/6/
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