SEMINÁRIO DE ANÁLISE E EDP - Alexandrov's Theorem Revisited

Alexandrov's Theorem Revisited
Expositor: Matias Delgadino
Instituição: Imperial College London
Data e Horário: 30/10/18 | 15:00hs

RESUMO: In this talk we will introduce the framework of sets of finite perimeter and we show that, among sets of finite perimeter, balls are the only volumeconstrained critical points of the perimeter functional. We will explore possible applications of this result to the volume-preserving mean curvature flow. The proof of the result utilises heavily the Heintze-Karcher inequality, which relates the volume of a open set with the integral of the reciprocal of the mean curvature on the boundary of the set. This is joint work with Francesco Maggi