Ricci curvature for metric-measure spaces via optimal transport
arXiv:math/0412127
Abstract
We define a notion of a measured length space X having nonnegative N-Ricci curvature, for N finite, or having infinity-Ricci curvature bounded below by K, for K a real number. The definitions are in terms of the displacement convexity of certain functions on the associated Wasserstein space P_2(X) of probability measures. We show that these properties are preserved under measured Gromov-Hausdorff limits. We give geometric and analytic consequences.
arXiv commentfinal version, Appendix D of previous version to appear separately
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