The rigidity of eigenfunctions' gradient estimates
Differential Geometry
2024-12-25 v2 Analysis of PDEs
Spectral Theory
Abstract
On compact Riemannian manifolds with non-negative Ricci curvature and smooth (possibly empty), convex (or mean convex) boundary, if the sharp Li-Yau type gradient estimate of an Neumann (or Dirichlet) eigenfunction holds at some non-critical points of the eigenfunction; we show that the manifold is isometric to the product of one lower dimension manifold and a round circle (or a line segment).
Cite
@article{arxiv.2405.05517,
title = {The rigidity of eigenfunctions' gradient estimates},
author = {Guoyi Xu and Xiaolong Xue},
journal= {arXiv preprint arXiv:2405.05517},
year = {2024}
}
Comments
to appear in Mathematische Zeitschrift