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SUMMARY:Vladimir Zolotov (SPbU)
DTSTART:20200423T130000Z
DTEND:20200423T150000Z
DTSTAMP:20260404T111248Z
UID:geomspb/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/geoms
 pb/1/">Bi-Lipschitz embeddings of self-contracted curves into Euclidean sp
 aces</a>\nby Vladimir Zolotov (SPbU) as part of A.D. Alexandrov Geometry S
 eminar\n\n\nAbstract\nThe question about characterization of metric spaces
  allowing bi-Lipschitz embeddings into Euclidean spaces is notoriously har
 d. To simplify the situation we deal with a 1-dimensional version of this 
 question. Namely we prove that a doubling metric space can be embedded int
 o Euclidean space under assumption that it can be presented as an image of
  a weakly self-contracting curve. (We say that a curve Г is weakly self-c
 ontracting if there exist K > 0 such that for every x < y < z < w in the d
 omain of the curve we have |Г(y)Г(z)| < K|Г(x)Г(w)|\, where |AB| denot
 es the distance between A and B.)\n
LOCATION:https://stable.researchseminars.org/talk/geomspb/1/
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