Matrix Li-Yau-Hamilton Estimates for Nonlinear Heat Equations

2019/11/01 by Xin-An Ren, Ren, Xin-An
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1911.00505

openalex publication_date 2019/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we are concerned with the matrix Li-Yau-Hamilton estimates for nonlinear heat equations. Firstly, we derive such estimate on a Kähler manifold with a fixed Kähler metric. Then we consider the estimate on Kähler manifolds with Kähler metrics evolving under the rescaled Kähler-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 Kähler manifolds.

Citations

• On the parabolic kernel of the Schrödinger operator
• The yamabe flow on locally conformally flat manifolds with positive ricci curvature
• New differential Harnack inequalities for nonlinear heat equations

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• Matrix Li-Yau-Hamilton Estimates under Kähler-Ricci Flow
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• Matrix Li-Yau-Hamilton estimates under Ricci Flow and parabolic frequency
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