Calculus of Variations and Geometric Measure Theory

A. Figalli - Y. H. Kim - R. J. McCann

On supporting hyperplanes to convex bodies

created by figalli on 10 Jun 2013


Accepted Paper

Inserted: 10 jun 2013
Last Updated: 10 jun 2013

Journal: Methods Appl. Anal.
Year: 2013


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.