On supporting hyperplanes to convex bodies
Analysis of PDEs
2011-07-07 v1 Classical Analysis and ODEs
Differential Geometry
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-Amp\`ere type equations arising in optimal transportation.
Cite
@article{arxiv.1107.1016,
title = {On supporting hyperplanes to convex bodies},
author = {Alessio Figalli and Young-Heon Kim and Robert J. McCann},
journal= {arXiv preprint arXiv:1107.1016},
year = {2011}
}
Comments
12 pages, 3 figures