Matrix Li-Yau-Hamilton estimates under Ricci Flow and parabolic frequency
Differential Geometry
2023-07-20 v2 Analysis of PDEs
Abstract
In this paper we prove matrix Li-Yau-Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply such estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature.
Keywords
Cite
@article{arxiv.2306.10143,
title = {Matrix Li-Yau-Hamilton estimates under Ricci Flow and parabolic frequency},
author = {Xiaolong Li and Qi S. Zhang},
journal= {arXiv preprint arXiv:2306.10143},
year = {2023}
}
Comments
39 pages. All comments are welcome. Theorem 1.4 and Section 7 added