Sharp Spectral Gap and Li-Yau's Estimate on Alexandrov Spaces
Differential Geometry
2012-05-29 v2 Analysis of PDEs
Metric Geometry
Abstract
In the previous work [35], the second and third authors established a Bochner type formula on Alexandrov spaces. The purpose of this paper is to give some applications of the Bochner type formula. Firstly, we extend the sharp lower bound estimates of spectral gap, due to Chen-Wang [9, 10] and Bakry-Qian [6], from smooth Riemannian manifolds to Alexandrov spaces. As an application, we get an Obata type theorem for Alexandrov spaces. Secondly, we obtain (sharp) Li-Yau's estimate for positve solutions of heat equations on Alexandrov spaces.
Cite
@article{arxiv.1102.4159,
title = {Sharp Spectral Gap and Li-Yau's Estimate on Alexandrov Spaces},
author = {Zhongmin Qian and Hui-Chun Zhang and Xi-Ping Zhu},
journal= {arXiv preprint arXiv:1102.4159},
year = {2012}
}
Comments
19 pages, final version, to appear in Math. Z