Conditions for existence of single valued optimal transport maps on convex boundaries with nontwisted cost

Seonghyeon Jeong, Jun Kitagawa

We prove that if $\Omega \subset {\mathbb{R}}^{n+1}$ is a (not necessarily strictly) convex, $C^1$ domain, and $\mu$ and $\bar{\mu }$ are probability measures absolutely continuous with respect t…