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Ricci curvature for metric-measure spaces via optimal transport

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arxiv math/0412127 v4 pith:6HLJCO76 submitted 2004-12-07 math.DG

Ricci curvature for metric-measure spaces via optimal transport

John Lott , Cedric Villani This is my paper
classification math.DG
keywords curvaturehavingmeasuredspaceanalyticassociatedbelowbounded
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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.

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