Weak formulation of the MTW condition and convexity properties of potentials

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.

Cited by in corpus (1)

• Synthetic MTW conditions and their equivalence under mild regularity assumption on the cost function