DG-MP-PDE Seminar: Young-Heon Kim

Abstract

 

Given a convex set and an interior point close to the boundary, we prove the existence of a supporting hyperplane whose distance to the point is controlled, in a dimensionally quantified way, by the thickness of the convex set in the orthogonal direction. This result has important applications in the regularity theory for Monge-Ampère type equations arising in optimal transportation. This is joint work with Alessio Figalli and Robert McCann.