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SUMMARY:Vladimir Zolotov (SPbU)
DTSTART:20200423T130000Z
DTEND:20200423T150000Z
DTSTAMP:20260422T225819Z
UID:geomspb/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/geomspb/1/">
 Bi-Lipschitz embeddings of self-contracted curves into Euclidean spaces</a
 >\nby Vladimir Zolotov (SPbU) as part of A.D. Alexandrov Geometry Seminar\
 n\n\nAbstract\nThe question about characterization of metric spaces allowi
 ng bi-Lipschitz embeddings into Euclidean spaces is notoriously hard. To s
 implify the situation we deal with a 1-dimensional version of this questio
 n. Namely we prove that a doubling metric space can be embedded into Eucli
 dean space under assumption that it can be presented as an image of a weak
 ly self-contracting curve. (We say that a curve Г is weakly self-contract
 ing if there exist K > 0 such that for every x < y < z < w in the domain o
 f the curve we have |Г(y)Г(z)| < K|Г(x)Г(w)|\, where |AB| denotes the 
 distance between A and B.)\n
LOCATION:https://researchseminars.org/talk/geomspb/1/
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