BAKRY-EMERY CURVATURE-DIMENSION CONDITION AND RIEMANNIAN RICCI CURVATURE BOUNDS
BAKRY-EMERY CURVATURE-DIMENSION CONDITION AND RIEMANNIAN RICCI CURVATURE BOUNDS
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DOI：
10.1214/14-aop907
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发表时间：
2015-01-01
影响因子：
2.3
通讯作者：
Savare, Giuseppe
中科院分区：
文献类型：
--
作者：
Ambrsio, Luigi;Gigli, Nicola;Savare, Giuseppe
本文的目的是弥合Bakry-Emery和Lott-Sturm-Villani方法之间的差距，给出Ricci曲率下界的综合和抽象概念，我们从一个强局部Dirichlet形式出发，在一个Polish测度空间（X，m）中引入一个Carre du champ F和一个导致X的原始拓扑的标准距离de.我们首先刻画了一类特殊的黎曼能量测度空间，其中f与de诱导的Cheeger能量一致，且每个函数f具有Gamma（f）
The aim of the present paper is to bridge the gap between the Bakry-Emery and the Lott-Sturm-Villani approaches to provide synthetic and abstract notions of lower Ricci curvature bounds.We start from a strongly local Dirichlet form epsilon admitting a Carre du champ F in a Polish measure space (X, m) and a canonical distance de that induces the original topology of X. We first characterize the distinguished class of Riemannian Energy measure spaces, where epsilon coincides with the Cheeger energy induced by de and where every function f with Gamma (f)