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.
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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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