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SUMMARY:Dennis Kriventsov (Rutgers University)
DTSTART:20211015T190000Z
DTEND:20211015T200000Z
DTSTAMP:20260423T022632Z
UID:VCU_ALPS/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCU_ALPS/9/"
 >Stability for Faber-Krahn inequalities and the ACF formula</a>\nby Dennis
  Kriventsov (Rutgers University) as part of VCU ALPS (Analysis\, Logic\, a
 nd Physics Seminar)\n\n\nAbstract\nThe Faber-Krahn inequality states that 
 the first Dirichlet eigenvalue of the Laplacian on a domain is greater tha
 n or equal to that of a ball of the same volume (and if equality holds\, t
 hen the domain is a translate of a ball). Similar inequalities are availab
 le on other manifolds where balls minimize perimeter over sets of a given 
 volume. I will present a new sharp stability theorem for such inequalities
 : if the eigenvalue of a set is close to a ball\, then the first eigenfunc
 tion of that set must be close to the first eigenfunction of a ball\, with
  the closeness quantified in an optimal way. I will also explain an applic
 ation of this to the behavior of the Alt-Caffarelli-Friedman monotonicity 
 formula\, which has implications for free boundary problems with multiple 
 phases. This is based on recent joint work with Mark Allen and Robin Neuma
 yer.\n
LOCATION:https://researchseminars.org/talk/VCU_ALPS/9/
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