Harnack estimates for conjugate heat kernel on evolving manifolds

被引：16

作者：

Cao, Xiaodong ^{[1
]}

Guo, Hongxin ^{[2
]}

Hung Tran ^{[3
]}

机构：

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

[2] Wenzhou Univ, SMIS, Wenzhou 325035, Zhejiang, Peoples R China

[3] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

来源：

MATHEMATISCHE ZEITSCHRIFT | 2015年 / 281卷 / 1-2期

关键词：

GEOMETRIC FLOWS; RICCI FLOW; ENTROPY;

D O I：

10.1007/s00209-015-1479-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are able to obtain a Harnack inequality. Our abstract formulation provides a unified framework for some known results, in particular including corresponding results of Ni (J Geom Anal 14(1): 87-100, 2004), Perelman (arXiv: math. DG/0211159, 2002) and Tran (arXiv: 1211.6448, 2012) as special cases. Moreover, it leads to new results in the setting of Ricci-Harmonic flow and mean curvature flow in Lorentzian manifolds with nonnegative sectional curvature.

引用

页码：201 / 214

页数：14

共 50 条

[31] AN INTERPOLATING HARNACK INEQUALITY FOR NONLINEAR HEAT EQUATION ON A SURFACE [J].

Guo, Hongxin ;

Zhu, Chengzhe .

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2021, 58 (04) :909-914

[32] OPTIMAL TRANSPORTATION AND MONOTONIC QUANTITIES ON EVOLVING MANIFOLDS [J].

Huang, Hong .

PACIFIC JOURNAL OF MATHEMATICS, 2010, 248 (02) :305-316

[33] Parabolic Gradient Estimates and Harnack Inequalities for a Nonlinear Equation Under The Ricci Flow [J].

Liangdi Zhang .

Bulletin of the Brazilian Mathematical Society, New Series, 2021, 52 :77-99

[34] Parabolic Gradient Estimates and Harnack Inequalities for a Nonlinear Equation Under The Ricci Flow [J].

Zhang, Liangdi .

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2021, 52 (01) :77-99

[35] EXPONENTIAL CONTRACTION IN WASSERSTEIN DISTANCE ON STATIC AND EVOLVING MANIFOLDS [J].

Cheng, Li-Juan ;

Thalmaier, Anton ;

Zhang, Shao-Qin .

REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 2021, 66 (01) :107-129

[36] Some Gradient Estimates and Liouville Properties of the Fast Diffusion Equation on Riemannian Manifolds [J].

Wang, Wen ;

Xie, Rulong ;

Zhang, Pan .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2021, 42 (04) :529-550

[37] Evolution systems of measures and semigroup properties on evolving manifolds [J].

Cheng, Li-Juan ;

Thalmaier, Anton .

ELECTRONIC JOURNAL OF PROBABILITY, 2018, 23

[38] Harnack estimates for geometric flows, applications to Ricci flow coupled with harmonic map flow [J].

Guo, Hongxin ;

He, Tongtong .

GEOMETRIAE DEDICATA, 2014, 169 (01) :411-418

[39] Harnack estimates for geometric flows, applications to Ricci flow coupled with harmonic map flow [J].

Hongxin Guo ;

Tongtong He .

Geometriae Dedicata, 2014, 169 :411-418

[40] Differential Harnack inequalities for heat equations with potentials under geometric flows [J].

Fang, Shouwen .

ARCHIV DER MATHEMATIK, 2013, 100 (02) :179-189

← 1 2 3 4 5 →