HEAT KERNEL ESTIMATES UNDER THE RICCI-HARMONIC MAP FLOW

被引：3

作者：

Bailesteanu, Mihai ^{[1
]}

Tran, Hung ^{[2
]}

机构：

[1] Cent Connecticut State Univ, Dept Math, 120 Marcus White Hall, New Britain, CT 06052 USA

[2] Univ Calif Irvine, Dept Math, 440G Rowland Hall, Irvine, CA 92612 USA

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2017年 / 60卷 / 04期

关键词：

heat equation; heat kernel; Ricci flow; harmonic map; Sobolev embedding; differential Harnack inequality; EQUATION;

D O I：

10.1017/S0013091516000523

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper considers the Ricci flow coupled with the harmonic map flow between two manifolds. We derive estimates for the fundamental solution of the corresponding conjugate heat equation and we prove an analogue of Perelman's differential Harnack inequality. As an application, we find a connection between the entropy functional and the best constant in the Sobolev embedding theorem in R-n.

引用

页码：831 / 857

页数：27

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