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arXiv · 2409.10379

An improved Hamilton matrix estimates for the heat equation

Lang Qin·Qi S. Zhang
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Abstract

In this paper, we remove the assumption on the gradient of the Ricci curvature in Hamilton's matrix Harnack estimate for the heat equation on all closed manifolds, answering a question which has been around since the 1990s. New ingredients include a recent sharp Li-Yau estimate, construction of a suitable vector field and various use of integral arguments, iteration and a little tensor algebra.

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Lang Qin, Qi S. Zhang. 2024-09-16. An improved Hamilton matrix estimates for the heat equation. https://arxiv.org/abs/2409.10379

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