Journal
TOHOKU MATHEMATICAL JOURNAL
Volume 63, Issue 4, Pages 855-876Publisher
TOHOKU UNIVERSITY
DOI: 10.2748/tmj/1325886291
Keywords
Nonlinear PDEs; optimal transport; riemannian geometry
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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.
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