On the Bakry-Emery Condition, the Gradient Estimates and the Local-to-Global Property of RCD*(K, N) Metric Measure Spaces

被引：0

作者：

Ambrosio, Luigi ^{[1
]}

Mondino, Andrea ^{[2
]}

Savare, Giuseppe ^{[3
]}

机构：

[1] Scuola Normale Super Pisa, Pisa, Italy

[2] ETH, Zurich, Switzerland

[3] Univ Pavia, Via Palestro 3, I-27100 Pavia, Italy

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2016年 / 26卷 / 01期

关键词：

Bakry-Emery curvature bounds; Dirichlet forms; CD; (K; N); spaces; Optimal transport; RICCI CURVATURE; GEOMETRY; SOBOLEV;

D O I：

10.1007/s12220-014-9537-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove higher summability and regularity of Gamma(f) for functions f in spaces satisfying the Bakry-Emery condition BE (K, infinity). As a byproduct, we obtain various equivalent weak formulations of BE(K, N) and we prove the Local-to-Global property of the RCD*(K, N) condition in locally compact metric measure spaces (X, d, m), without assuming a priori the non-branching condition on the metric space.

引用

页码：24 / 56

页数：33

共 17 条

[1] SELF-IMPROVEMENT OF THE BAKRY-EMERY CONDITION AND WASSERSTEIN CONTRACTION OF THE HEAT FLOW IN RCD(K, ∞) METRIC MEASURE SPACES
Savare, Giuseppe
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (04) : 1641 - 1661
[2] LOCAL GRADIENT ESTIMATES FOR HEAT EQUATION ON RCD*(k, n) METRIC MEASURE SPACES
Huang, Jia-Cheng
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (12) : 5391 - 5407
[3] Bakry-Emery Conditions on Almost Smooth Metric Measure Spaces
Honda, Shouhei
[J]. ANALYSIS AND GEOMETRY IN METRIC SPACES, 2018, 6 (01): : 129 - 145
[4] DIFFERENTIAL ONE-FORMS ON DIRICHLET SPACES AND BAKRY-EMERY ESTIMATES ON METRIC GRAPHS
Baudoin, Fabrice
Kelleher, Daniel J.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 371 (05) : 3145 - 3178
[5] Local Li-Yau's estimates on RCD*(K, N) metric measure spaces
Zhang, Hui-Chun
Zhu, Xi-Ping
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2016, 55 (04)
[6] On the Bakry–Émery Condition, the Gradient Estimates and the Local-to-Global Property of RCD∗(K,N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf{RCD}^*(K,N)$$\end{document} Metric Measure Spaces
Luigi Ambrosio
Andrea Mondino
Giuseppe Savaré
[J]. The Journal of Geometric Analysis, 2016, 26 (1): : 24 - 56
[7] Failure of the local-to-global property for CD(K, N) spaces
Rajala, Tapio
[J]. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2016, 15 : 45 - 68
[8] Obstacle Problems on RCD(K, N) Metric Measure Spaces
Lin, Sitan
[J]. ACTA MATHEMATICA SCIENTIA, 2023, 43 (05) : 1925 - 1944
[9] OBSTACLE PROBLEMS ON RCD(K,N)METRIC MEASURE SPACES
林锶坍
[J]. Acta Mathematica Scientia, 2023, 43 (05) : 1925 - 1944
[10] Obstacle Problems on RCD(K, N) Metric Measure Spaces
Sitan Lin
[J]. Acta Mathematica Scientia, 2023, 43 : 1925 - 1944

← 1 2 →