Sharp spectral gap and Li–Yau’s estimate on Alexandrov spaces
TLDR
In this paper, Zhang and Zhu give some applications of the Bochner type formula on Alexandrov spaces, and obtain (sharp) Li-Yau's estimate for positve solutions of heat equations.Abstract:
In the previous work (Zhang and Zhu in J Differ Geom, http://arxiv.org/pdf/1012.4233v3
, 2012), 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 and Wang (Sci Sin (A) 37:1–14, 1994), Chen and Wang (Sci Sin (A) 40:384–394, 1997) and Bakry–Qian (Adv Math 155:98–153, 2000), 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.read more
Citations
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