Gradient estimates for the heat equation under the Ricci flow

被引：103

作者：

Bailesteanu, Mihai ^{[2
]}

Cao, Xiaodong ^{[2
]}

Pulemotov, Artem ^{[1
,2
]}

机构：

[1] Univ Chicago, Dept Math, 5734 S Univ Ave, Chicago, IL 60637 USA

[2] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 258卷 / 10期

基金：

美国国家科学基金会;

关键词：

Ricci flow; Heat equation; Li-Yau inequality; Harnack inequality; Manifold with boundary; HARNACK INEQUALITIES; DEFORMATION; CURVATURE; MANIFOLDS; KERNEL;

D O I：

10.1016/j.jfa.2009.12.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper considers a manifold M evolving under the Ricci flow and establishes a series of gradient estimates for positive Solutions of the heat equation on M. Among other results, we prove Li-Yau-type inequalities in this context. We consider both the case where M is a complete manifold without boundary and the case where M is a compact manifold with boundary. Applications of our results include Harnack inequalities for the heat equation on M. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：3517 / 3542

页数：26

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