Weak formulation of the MTW condition and convexity properties of potentials

2020/07/06 by Loeper, G., Trudinger, N. S.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.02665

Abstract

We simplify the geometric interpretation of the weak Ma-Trudinger-Wang condition for regularity in optimal transportation and provide a geometric proof of the global c-convexity of locally c-convex potentials when the cost function c is only assumed twice differentiable.

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