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arXiv · 1911.00505

Matrix Li-Yau-Hamilton Estimates for Nonlinear Heat Equations

Xin-An Ren
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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 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.

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Xin-An Ren. 2019-11-01. Matrix Li-Yau-Hamilton Estimates for Nonlinear Heat Equations. https://arxiv.org/abs/1911.00505

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