Transport Inequalities, Gradient Estimates, Entropy and Ricci Curvature

Abstract

We present various characterizations of uniform lower bounds for the Ricci curvature of a smooth Riemannian manifoldM in terms of convexity properties of the entropy (considered as a function on the space of probability measures on M) as well as in terms of transportation inequalities for volume measures, heat kernels and Brownian motions and in terms of gradient estimates for the heat semigroup.

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@inproceedings{Sturm2003TransportIG, title={Transport Inequalities, Gradient Estimates, Entropy and Ricci Curvature}, author={K. Sturm}, year={2003} }