Ricci curvature for metric-measure spaces via optimal transport
Differential Geometry
2007-05-23 v4
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.
Keywords
Cite
@article{arxiv.math/0412127,
title = {Ricci curvature for metric-measure spaces via optimal transport},
author = {John Lott and Cedric Villani},
journal= {arXiv preprint arXiv:math/0412127},
year = {2007}
}
Comments
final version, Appendix D of previous version to appear separately