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Paper detail

On supporting hyperplanes to convex bodies

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.

preprint2011arXivOpen access
Alessio FigalliYoung-Heon KimRobert J. McCann
math.APmath.CAmath.DG
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Alessio FigalliYoung-Heon KimRobert J. McCann

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