Inserted: 8 mar 2008
Last Updated: 12 jan 2009
Journal: SIAM J. Math. Anal.
In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound.
Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is based on the Eulerian point of view recently introduced by Otto-Westdickenberg and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.
Keywords: displacement convexity, Optimal transport, Gradient flows, Ricci curvature