An improved Hamilton matrix estimates for the heat equation
Differential Geometry
2024-09-17 v1 Analysis of PDEs
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.
Cite
@article{arxiv.2409.10379,
title = {An improved Hamilton matrix estimates for the heat equation},
author = {Lang Qin and Qi S. Zhang},
journal= {arXiv preprint arXiv:2409.10379},
year = {2024}
}