# Analysis Seminar

#### Faber-Krahn Inequalities in Sharp Quantitative Form

Speaker: Guido de Phillipis, University of Lyon

Location: Warren Weaver Hall 1302

Date: Thursday, March 12, 2015, 11 a.m.

Synopsis:

In this talk we present a sharp quantitative improvement of the celebrated Faber-Krahn inequality. The latter asserts that balls uniquely minimize the ﬁrst eigenvalue of the Dirichlet-Laplacian, among sets with given volume. We prove that indeed more can be said: the diﬀerence between the ﬁrst eigenvalue λ(Ω) of a set Ω and that of a ball of the same volume controls the deviation from spherical symmetry of Ω. Moreover, such a control is the sharpest possible. This settles a conjecture by Bhattacharya, Nadirashvili and Weitsman.