Ricci curvature for metric-measure spaces via optimal transport

  title={Ricci curvature for metric-measure spaces via optimal transport},
  author={John Lott and C{\'e}dric Villani},
  journal={Annals of Mathematics},
We dene a notion of a measured length space X having nonnegative N-Ricci curvature, for N 2 [1;1), or having1-Ricci curvature bounded below byK, forK2 R. The denitions are in terms of the displacement convexity of certain functions on the associated Wasserstein metric space P2(X) of probability measures. We show that these properties are preserved under measured Gromov-Hausdor limits. We give geometric and analytic consequences. This paper has dual goals. One goal is to extend results about… Expand
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