Sharp Spectral Gap and Li-Yau's Estimate on Alexandrov Spaces

Details Sharp Spectral Gap and Li-Yau's Estimate on Alexandrov Spaces Sharp Spectral Gap and Li-Yau's Estimate on Alexandrov Spaces

2011-02-21

arxiv.org/abs/1102.4159v1

Mathematics

Differential Geometry

17 pages

Scientific paper

In the previous work [32], 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 [8, 9] and Bakry-Qian [5], 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.

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