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math.AP2011
On supporting hyperplanes to convex bodies
Alessio Figalli, Young-Heon Kim, Robert J. McCann
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 quan…
math.AP2011★ 9 cited
Hölder continuity and injectivity of optimal maps
Alessio Figalli, Young-Heon Kim, Robert J. McCann
Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth…