EVENT DETAILS AND ABSTRACT

Title: Minkowski estimates on critical and nodal sets of harmonic functions
Speaker: Daniele Valtorta
Speaker Info: EPFL Lausanne
Brief Description:
Special Note:
Abstract:

Given a nonconstant harmonic function, we obtain Minkowski bounds on its critical and almost critical set. The proof relies on a refined blow-up analysis for harmonic functions based on the properties of Almgren's frequency. With minor modifications, these estimates are valid also for solutions to a very general class of elliptic PDEs. Given the link between harmonic functions and eigenfunctions of the Laplacians, with the necessary modifications these results apply also to nodal and singular sets of eigenfunctions. This is joint work with Aaron Naber.