Differential Harnack Inequalities Under a Coupled Ricci Flow

被引：6

作者：

Wang, Lin Feng ^{[1
]}

机构：

[1] Nantong Univ, Sch Sci, Nantong 226007, Peoples R China

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2012年 / 15卷 / 04期

关键词：

Ricci flow; Differential inequality; Conjugate heat equation; Harnack inequality;

D O I：

10.1007/s11040-012-9115-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove several differential Harnack inequalities under a coupled Ricci flow. As applications, we get Harnack inequalities for positive solutions of backward heat-type equations with potentials under the coupled Ricci flow. We also derive Perelman's differential Harnack inequality for fundamental solution of the conjugate heat equation under the Ricci flow.

引用

页码：343 / 360

页数：18

共 17 条

[1]

Cao HD, 2006, ASIAN J MATH, V10, P165

[2] Differential Harnack estimates for backward heat equations with potentials under the Ricci flow [J].

Cao, Xiaodong .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (04) :1024-1038

[3] Rigidity of quasi-Einstein metrics [J].

Case, Jeffrey ;

Shu, Yu-Jen ;

Wei, Guofang .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2011, 29 (01) :93-100

[4]

HAMILTON RS, 1993, J DIFFER GEOM, V37, P225

[5] A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow [J].

Kuang, Shilong ;

Zhang, Qi S. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (04) :1008-1023

[6] ON THE PARABOLIC KERNEL OF THE SCHRODINGER OPERATOR [J].

LI, P ;

YAU, ST .

ACTA MATHEMATICA, 1986, 156 (3-4) :153-201

[7] Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds [J].

Li, XD .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2005, 84 (10) :1295-1361

[8]

List B., 2005, THESIS AER POSTDAM

[9] Some geometric properties of the Bakry-Emery-Ricci tensor [J].

Lott, J .

COMMENTARII MATHEMATICI HELVETICI, 2003, 78 (04) :865-883

[10]

Muller R., 2009, The Ricci flow coupled with harmonic map heat flow

← 1 2 →