Characterizations of the Upper Bound of Bakry-Emery Curvature

被引：0

作者：

Wu, Bo ^{[1
,2
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[2] Univ Bonn, Inst Appl Math, Endenicher Allee 60, D-53115 Bonn, Germany

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2020年 / 30卷 / 04期

关键词：

Bakry-Emery curvature; Functional inequality; Diffusion process; Path space; LOGARITHMIC SOBOLEV INEQUALITIES; PATH SPACES; RICCI CURVATURE; MANIFOLDS;

D O I：

10.1007/s12220-019-00222-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we will present characterizations for the upper bound of the Bakry-Emery curvature on a Riemannian manifold by using functional inequalities on the path space. Moreover, characterizations for general lower and upper bounds of Ricci curvature are also given, which extends the recent results derived by Naber (Characterizations of bounded Ricci curvature on smooth and nonsmooth spaces, arXiv:1306.6512v4) and Wang-Wu (Sci China Math 61:1407-1420, 2018). A crucial point of the present study is to use a symmetrization argument for the lower and upper bounds of Ricci curvature, and a localization technique.

引用

页码：3923 / 3947

页数：25

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