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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 |
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Vol. 338 (2025), No. 1, 19–34
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Abstract |
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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
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Mathematical Subject Classification
Primary: 53E20, 58J35
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Milestones
Received: 15 August 2024
Revised: 29 March 2025
Accepted: 16 May 2025
Published: 14 June 2025
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Authors |
| Sha Yao | |
| School of Mathematics and
Information Science Henan Polytechnic University Jiaozuo China |
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| Hao-Yue Liu | |
| School of Science Jiangsu Ocean University Lianyungang China |
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| Xin-An Ren | |
| School of Mathematics China University of Mining and Technology Xuzhou China |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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