00962nas a2200121   4500008004300000245008100043210006900124260000900193520056300202100001700765700002200782856003600804       2008                        en_Ud  00aEulerian calculus for the displacement convexity in the Wasserstein distance0 aEulerian calculus for the displacement convexity in the Wasserst  bSIAM3 aIn 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 and Westdickenberg [SIAM J. Math. Anal., 37 (2005), pp. 1227-1255] and on the metric characterization of the gradient flows generated by the functionals in the Wasserstein space.1 aDaneri, Sara1 aSavarè, Giuseppe  uhttp://hdl.handle.net/1963/3413