Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds
In this paper we continue the investigation of the regularity of optimal transport maps on Riemannian manifolds, in relation with the geometric conditions of Ma-Trudinger-Wang and the geometry of the cut locus. We derive some sufficient and some necessary conditions to ensure that the optimal transport map is always continuous. In dimension two, we can sharpen our result into a necessary and sufficient condition. We also provide some sufficient conditions for regularity, and review existing results.
Permanent link to this document: http://projecteuclid.org/euclid.tmj/1325886291
Digital Object Identifier: doi:10.2748/tmj/1325886291
Zentralblatt MATH identifier: 06016717
Mathematical Reviews number (MathSciNet): MR2872966