Some aspects of Cheng-Yau gradient estimates
Differential Geometry
2025-11-25 v1 Analysis of PDEs
Abstract
In this note, we extend the rigidity of Cheng-Yau gradient estimate in \cite{HXY} to surfaces with lower Ricci curvature bound. Motivated by these sharp Cheng-Yau gradient estimates, pointwise Cheng-Yau gradient estimates for higher dimensional Riemannian manifolds are obtained, and as their applications, monotonicity formulas for positive harmonic functions are obtained.
Cite
@article{arxiv.2511.19042,
title = {Some aspects of Cheng-Yau gradient estimates},
author = {Qixuan Hu and Chengjie Yu},
journal= {arXiv preprint arXiv:2511.19042},
year = {2025}
}