Weak formulation of the MTW condition and convexity properties of potentials
Analysis of PDEs
2020-09-09 v2
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 -convex potentials when the cost function is only assumed twice differentiable.
Keywords
Cite
@article{arxiv.2007.02665,
title = {Weak formulation of the MTW condition and convexity properties of potentials},
author = {G. Loeper and N. S. Trudinger},
journal= {arXiv preprint arXiv:2007.02665},
year = {2020}
}