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Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance
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Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance
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Journal Article
Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance
2008
Overview
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.
Publisher
Society for Industrial and Applied Mathematics
