Estimates for the Critical Set of Harmonic Functions

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari
Ore 15:00

Relatore:

• Daniele Valtorta (EPFL, Losanna)

Abstract:
Given a harmonic function defined on the unit ball of R^n, we discuss techniques to obtain effective volume estimates on the tubular neighborhood of its critical sets.
For the proof, we use a technique recently introduced by proff. Jeff Cheeger and Aaron Naber, called quantitative stratification technique. It is based on approximate symmetries of the function u at different scales. Studying how these approximate symmetries interact with each other, we obtain the effective volume estimates. In the second part of the talk, we discuss recent improvements on these results and extensions to nodal sets. These results are described in a preprint available on arXiv, joint work with Aaron Naber and Jeff Cheeger.

Referente: Francesco Serra Cassano