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On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking Ricci solitons

Authors
  • Futaki, Akito
  • Li, Haizhong
  • Li, Xiang-Dong
Type
Preprint
Publication Date
Feb 27, 2012
Submission Date
Nov 28, 2011
Identifiers
arXiv ID: 1111.6364
Source
arXiv
License
Yellow
External links

Abstract

We prove a lower bound estimate for the first non-zero eigenvalue of the Witten-Laplacian on compact Riemannian manifolds. As an application, we derive a lower bound estimate for the diameter of compact gradient shrinking Ricci solitons. Our results improve some previous estimates which were obtained by the first author and Y. Sano in [12], and by B. Andrews and L. Ni in [1]. Moreover, we extend the diameter estimate to compact self-similar shrinkers of mean curvature flow.

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