The rigidity and stability of gradient estimates
Differential Geometry
2024-11-05 v1
Abstract
In this note, we obtain the rigidity of the sharp Cheng-Yau gradient estimate for positive harmonic functions on surfaces with nonegative Gaussian curvature, the rigidity of the sharp Li-Yau gradient estimate for positive solutions to heat equations and the related estimates for Dirichlet Green's functions on Riemannian manifolds with nonnegative Ricci curvature. Moreover, we also obtain the corresponding stability results.
Cite
@article{arxiv.2208.02944,
title = {The rigidity and stability of gradient estimates},
author = {Qixuan Hu and Guoyi Xu and Chengjie Yu},
journal= {arXiv preprint arXiv:2208.02944},
year = {2024}
}
Comments
to appear in a special issue of J. Geom. Anal, in honor of Peter Li's 70th birthday