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Matrix Li–Yau–Hamilton estimates for nonlinear heat equations under geometric flows

Sha Yao, Hao-Yue Liu and Xin-An Ren

Vol. 338 (2025), No. 1, 19–34
Abstract

We are concerned with the matrix Li–Yau–Hamilton estimates for nonlinear heat equations. Firstly, we derive such an estimate for positive solutions to the nonlinear heat equations under the Ricci flow. Then we consider the estimates for positive solutions to the nonlinear heat equations and the nonlinear backward conjugate heat equations under the Kähler–Ricci flow.

Keywords
Li–Yau–Hamilton estimate, nonlinear heat equation, Ricci flow, Kähler–Ricci flow
Mathematical Subject Classification
Primary: 53E20, 58J35
Milestones
Received: 15 August 2024
Revised: 29 March 2025
Accepted: 16 May 2025
Published: 14 June 2025
Authors
Sha Yao
School of Mathematics and Information Science
Henan Polytechnic University
Jiaozuo
China
Hao-Yue Liu
School of Science
Jiangsu Ocean University
Lianyungang
China
Xin-An Ren
School of Mathematics
China University of Mining and Technology
Xuzhou
China

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