Geodesic
Ricci curvature for metric-measure spaces via optimal transport
John Lott1 ; Cedric Villani2
1 Department of Mathematics<br/>University of Michigan<br/>Ann Arbor, MI 48109<br/>United States
2 UMPA (UMR CNRS 5669)<br/>École Normale Supérieure de Lyon<br/>69364 Lyon<br/>France
Annals of mathematics, Tome 169 (2009) no. 3, pp. 903-991.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We define a notion of a measured length space $X$ having nonnegative $N$-Ricci curvature, for $N \in [1, \infty)$, or having $\infty$-Ricci curvature bounded below by $K$, for $K \in \mathbb{R}$. The definitions are in terms of the displacement convexity of certain functions on the associated Wasserstein metric 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.
DOI : 10.4007/annals.2009.169.903

John Lott 1 ; Cedric Villani 2

1 Department of Mathematics<br/>University of Michigan<br/>Ann Arbor, MI 48109<br/>United States
2 UMPA (UMR CNRS 5669)<br/>École Normale Supérieure de Lyon<br/>69364 Lyon<br/>France 
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John Lott; Cedric Villani. Ricci curvature for metric-measure spaces via optimal transport. Annals of mathematics, Tome 169 (2009) no. 3, pp. 903-991. doi : 10.4007/annals.2009.169.903. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.903/

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