Matrix Li-Yau-Hamilton estimates for nonlinear heat equations

被引：0

作者：

Ren, Xin-An ^{[1
]}

机构：

[1] China Univ Min & Technol, Dept Math, Xuzhou 221116, Jiangsu, Peoples R China

来源：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2024年 / 32卷 / 05期

关键词：

COMPLETE KAHLER-MANIFOLDS; HARNACK INEQUALITIES; PLURISUBHARMONIC-FUNCTIONS; RICCI FLOW; MONOTONICITY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we are concerned with the matrix Li-Yau-Hamilton estimates for nonlinear heat equations. Firstly, we derive such an estimate on a Kahler manifold with a fixed Kahler metric. Then we consider the estimate on Kahler manifolds with Kahler metrics evolving under the rescaled Kahler-Ricci flow. Both of the estimates are generalized to constrained cases. Finally, we extend the estimtes to more general nonlinear heat equations on both Riemannian manifolds and Kahler manifolds.

引用

页码：1403 / 1434

页数：32