a1 Centre de Mathématiques Laurent Schwartz, UMR 7640, École Polytechnique, 91128 Palaiseau, France. firstname.lastname@example.org
a2 University of Bordeaux, France. email@example.com
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.
(Received July 4 2009)
(Revised October 13 2009)
(Online publication March 31 2010)
Mathematics Subject Classification:
* N. Gigli was partially financed by KAM Faible, ANR-07-BLAN-0361.