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SUMMARY:Asaf Shachar (The Hebrew University of Jerusalem)
DTSTART:20211102T180000Z
DTEND:20211102T190000Z
DTSTAMP:20260423T035036Z
UID:OSGA/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSGA/86/">No
 n-Euclidean elasticity: Embedding surfaces with minimal distortion</a>\nby
  Asaf Shachar (The Hebrew University of Jerusalem) as part of Online Semin
 ar "Geometric Analysis"\n\n\nAbstract\nGiven two dimensional Riemannian ma
 nifolds $M\,N$\, I will present a sharp lower bound on the elastic energy 
 (distortion) of embeddings $f:M \\to N$\, in terms of the areas' discrepan
 cy of $M\,N$.\n\nThe minimizing maps attaining this bound go through a pha
 se transition when the ratio of areas is $1/4$: The homotheties are the un
 ique energy minimizers when the ratio $\\frac{\\operatorname{Vol}(N)}{\\op
 eratorname{Vol}(M)} \\ge 1/4$\, and they cease being minimizers when $\\fr
 ac{\\operatorname{Vol}(N)}{\\operatorname{Vol}(M)} $ gets below $1/4$.\n\n
 I will describe explicit minimizers in the non-trivial regime $\\frac{\\op
 eratorname{Vol}(N)}{\\operatorname{Vol}(M)} < 1/4$ when $M\,N$ are disks\,
  and give a proof sketch of the lower bound. If time permits\, I will disc
 uss the stability of minimizers.\n
LOCATION:https://researchseminars.org/talk/OSGA/86/
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