| Issue |
ESAIM: COCV
Volume 17, Number 3, July-September 2011
|
|
|---|---|---|
| Page(s) | 648 - 653 | |
| DOI | https://doi.org/10.1051/cocv/2010011 | |
| Published online | 31 March 2010 | |
Local semiconvexity of Kantorovich potentials on non-compact manifolds*
1
Centre de Mathématiques Laurent Schwartz, UMR 7640, École
Polytechnique, 91128 Palaiseau, France. figalli@math.polytechnique.fr
2
University of Bordeaux, France. nicolagigli@googlemail.com
Received:
4
July
2009
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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