Inserted: 9 oct 2009
Last Updated: 13 oct 2009
Journal: ESAIM Control Optim. Calc. Var.
We prove that any Kantorovich potential for the cost function $c=d^2/2$ 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 $\mu$-measure as soon as the starting measure $\mu$ does not charge $n-1$-dimensional rectifiable sets.