Methods and Applications of Analysis
Volume 20 (2013)
On supporting hyperplanes to convex bodies
Pages: 261 – 272
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.
convex bodies, supporting hyperplanes
2010 Mathematics Subject Classification
35J96, 52A20, 52A40