English

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 cc-convex potentials when the cost function cc 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}
}