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Joint Princeton-Rutgers Seminar on Geometric PDE's

Stability for Faber-Krahn inequalities and the ACF formula

Dennis Kriventsov, Rutgers University

Location:  zoom
Date & time: Monday, 24 May 2021 at 2:15PM - 3:15PM

Abstract: The Faber-Krahn inequality states that the first Dirichlet eigenvalue of the Laplacian on a domain is greater than or equal to that of a ball of the same volume (and if equality holds, then the domain is a translate of a ball). Similar inequalities are available on other manifolds where balls minimize perimeter over sets of a given volume. I will discuss the stability problem for such inequalities: if the eigenvalue of a set is close to a ball, how similar to a ball must the set look like? I will also explain an application of sufficiently strong stability results to quantifying 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 Neumayer.

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