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Title: Lower bounds on the inner radius of nodal domains of Laplace eigenfunctions

Abstract: Consider nodal domains (connected components of the set where a function is non-zero) of Laplace eigenfunctions on a closed compact manifold. By Faber-Krahn's inequality, a nodal domain cannot contain a ball of size C 位^{-1/2}. However, it is harder to find lower bounds on the size of the biggest ball that can be contained inside a nodal domain.
In this talk, I will discuss a recent result (with Dan Mangoubi) that shows that it is always possible to find a ball of size C 位^{-1/2} (log 位)^{-(d-2)/2}. The proof uses a mixture of old and new techniques, some of which come from Brownion motion / heat kernel estimates, while others come from recent advances on solutions to elliptic equations.

Where: CRM, Universit茅 de Montr茅al, Pavillon Andr茅-Aisenstadt, room 4186 or

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Meeting ID: 895 2873 0384

Passcode: 077937