The first Dirichlet eigenvalue and the width
Differential Geometry
2024-11-05 v2 Analysis of PDEs
Spectral Theory
Abstract
For a geodesic ball with non-negative Ricci curvature and mean convex boundary, it is known that the first Dirichlet eigenvalue of this geodesic ball has a sharp lower bound in term of its radius. We show a quantitative explicit inequality, which bounds the width of geodesic ball in terms of the spectral gap between the first Dirichlet eigenvalue and the corresponding sharp lower bound.
Keywords
Cite
@article{arxiv.2407.10027,
title = {The first Dirichlet eigenvalue and the width},
author = {Guoyi Xu},
journal= {arXiv preprint arXiv:2407.10027},
year = {2024}
}
Comments
With an appendix by Zichang Liu, to appear in J. Funct. Anal