Ricci curvature for metric-measure spaces via optimal transport

• 成果类型: Article
• 署名作者: Lott, John; Villani, Cedric
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.169.903
• 发表日期: 2009
• 页码: 903-991
• 关键词: logarithmic sobolev inequalities; RIEMANNIAN-MANIFOLDS; EQUATIONS; geometry; MAPS

摘要

We define a notion of a measured length space X having nonnegative N-Ricci curvature, for N is an element of [1, infinity), or having infinity-Ricci curvature bounded below by K, for K is an element of 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.