Volume 17, Number 3, July-September 2011
|Page(s)||648 - 653|
|Published online||31 March 2010|
Local semiconvexity of Kantorovich potentials on non-compact manifolds*
Centre de Mathématiques Laurent Schwartz, UMR 7640, École
Polytechnique, 91128 Palaiseau, France. email@example.com
2 University of Bordeaux, France. firstname.lastname@example.org
Revised: 13 October 2009
We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex in the “region of interest”, without any compactness assumption on M, nor any assumption on its curvature. Such a region of interest is of full μ-measure as soon as the starting measure μ does not charge n – 1-dimensional rectifiable sets.
Mathematics Subject Classification: 49Q20 / 35J96
Key words: Kantorovich potential / optimal transport / regularity
© EDP Sciences, SMAI, 2010
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