On supporting hyperplanes to convex bodies

Details On supporting hyperplanes to convex bodies On supporting hyperplanes to convex bodies

2011-07-06

arxiv.org/abs/1107.1016v1

Mathematics

Analysis of PDEs

12 pages, 3 figures

Scientific paper

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.

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