Iosif Polterovich, Universite de Montreal – Analysis & PDE Seminar

Title: Isoperimetric inequalities for Laplace eigenvalues on surfaces: some recent developments

Abstract: Isoperimetric inequalities for Laplace eigenvalues have a long history, going back to the celebrated Rayleigh-Faber-Krahn inequality for the fundamental tone. Still, many basic questions remain unanswered, particularly, for higher eigenvalues. In the talk I will give an overview of some recent developments in the study of isoperimetric inequalities for eigenvalues on compact surfaces with a Riemannian metric. In particular, I will discuss a solution of a conjecture posed by N. Nadirashvili in 2002 regarding the maximization of higher Laplace-Beltrami eigenvalues on the sphere.
The talk is based on a joint work with M. Karpukhin, N. Nadirashvili and A. Penskoi.