Matrix Li-Yau-Hamilton Estimates for Nonlinear Heat Equations

In this paper we are concerned with the matrix Li-Yau-Hamilton estimates for nonlinear heat equations. Firstly, we derive such estimate on a K\"{a}hler manifold with a fixed K\"{a}hler metric. Then we consider the estimate on K\"{a}hler manifolds with K\"{a}hler metrics evolving...

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Bibliographic Details
Published in:arXiv.org 2019-11
Main Author: Xin-An, Ren
Format: Article
Language:English
Subjects:
Estimates
Mathematical analysis
Nonlinear equations
Riemann manifold
Thermodynamics
Online Access:Get full text
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Summary:In this paper we are concerned with the matrix Li-Yau-Hamilton estimates for nonlinear heat equations. Firstly, we derive such estimate on a K\"{a}hler manifold with a fixed K\"{a}hler metric. Then we consider the estimate on K\"{a}hler manifolds with K\"{a}hler metrics evolving under the rescaled K\"{a}hler-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 K\"{a}hler manifolds.
ISSN:2331-8422