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UID:20260624T113021EDT-5364Rz8Jsp@132.216.98.100
DTSTAMP:20260624T153021Z
DESCRIPTION:Title: Homogenization of Steklov problems with applications to 
 sharp isoperimetric bounds\, part I\n	Abstract: The question to find the be
 st upper bound for the first nonzero Steklov eigenvalue of a planar domain
  goes back to Weinstock\, who proved in 1954 that the first nonzero perime
 ter-normalized Steklov eigenvalue of a simply-connected planar domain is 2
 *pi\, with equality iff the domain is a disk. In a recent joint work with 
 Mikhail Karpukhin and and Jean Lagacé\, we were able to let go of the simp
 le connectedness assumption. We constructed a family of domains for which 
 the perimeter-normalized first eigenvalue tends to 8π. In combination with
  Kokarev's bound from 2014\, this solves the isoperimetric problem complet
 ely for the first nonzero eigenvalue. The domains are obtained by removing
  small geodesic balls that are asymptotically densely periodically distrib
 uted as their radius tends to zero. The goal of this talk will be to surve
 y recent work on homogenisation of the Steklov problem which lead to the a
 bove result. On the way we will see that many spectral problems can be app
 roximated by Steklov eigenvalues of perforated domains. A surprising conse
 quence is the existence of free boundary minimal surfaces immersed in the 
 unit ball by first Steklov eigenfunctions and with area strictly larger th
 an 2*pi. This talk is based on joint work with Antoine Henrot (U. de Lorra
 ine)\, Mikhail Karpukhin (UCI) and Jean Lagacé(UCL).\n	\n	 \n
DTSTART:20200501T170000Z
DTEND:20200501T180000Z
SUMMARY:Alexandre Girouard (Universite Laval)
URL:/mathstat/channels/event/alexandre-girouard-univer
 site-laval-321866
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