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arXiv · 2511.19042

Some aspects of Cheng-Yau gradient estimates

Qixuan Hu·Chengjie Yu
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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.

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Qixuan Hu, Chengjie Yu. 2025-11-24. Some aspects of Cheng-Yau gradient estimates. https://arxiv.org/abs/2511.19042

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