MENU

You are here

Eulerian calculus for the displacement convexity in the Wasserstein distance

TitleEulerian calculus for the displacement convexity in the Wasserstein distance
Publication TypeJournal Article
Year of Publication2008
AuthorsDaneri, S, Savare\', G
JournalSIAM J. Math. Anal. 40 (2008) 1104-1122
Abstract

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 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.

URLhttp://hdl.handle.net/1963/3413
DOI10.1137/08071346X

Sign in