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SUMMARY:Alexandre Girouard (Université de Laval)
DTSTART:20220422T150000Z
DTEND:20220422T161500Z
DTSTAMP:20260423T022741Z
UID:CIRGET/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CIRGET/65/">
 Steklov eigenvalues\, homogenization and free boundary minimal surfaces</a
 >\nby Alexandre Girouard (Université de Laval) as part of CRM - Séminair
 e du CIRGET / Géométrie et Topologie\n\n\nAbstract\nIt has been known si
 nce classical antiquity that disks have the largest area among planar figu
 res of prescribed perimeter. Nevertheless\, a rigorous proof was only give
 n around the end of the 19th century. During the 20th century\, area and p
 erimeter were replaced by many other analytic and geometric quantities\, a
 nd the geometric setting has been vastly enlarged. In this talk we will be
  interested in two such isoperimetric-type problems:\n\n(A) Free boundary 
 minimal surfaces\nThe minimization of area for surfaces in balls\, with th
 eir boundary that are constrained to live on the boundary sphere (free bou
 ndary minimal surfaces).\n\nB) Isoperimetric problem for Steklov eigenvalu
 es\nThe maximization of the spectral gap of Dirichlet-to-Neumann operators
  for surfaces with prescribed perimeter.\n\nFor domains in the unit sphere
  and planar domains\, I will describe the complete solution of problem (B)
 . It is based on the theory of homogenization by perforation\, a topic whi
 ch comes from applied and industrial mathematics. Then\, using work of Fra
 ser and Schoen\, I will show how this solution leads to the construction o
 f new free boundary minimal surfaces in the unit 3-ball that have area lar
 ger than was previously thought possible.\n\nThis talk is based on joint w
 ork with Antoine Henrot\, Mikhail Karpukhin and Jean Lagacé.\n
LOCATION:https://researchseminars.org/talk/CIRGET/65/
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