2008/01/01 by Sara Daneri, Giuseppe Savaré, Giuseppe Savare · 3 citations
Mathematics · #Class (philosophy) #Convexity #Curvature #Displacement (psychology) #Eulerian path #Geometric Analysis and Curvature Flows #Manifold (fluid mechanics) #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Ricci curvature #Riemannian manifold #Wasserstein metric #math.AP #math.DG #msc:49J40 #msc:58J35
paper · pdf · doi:10.1137/08071346x
published as SIAM J. Math. Anal. 40 (2008), 1104-1122
openalex publication_date 2008/01/01 · arxiv created 2008/01/16 · arxiv updated 2014/09/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.