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On second variation of Perelman's Ricci shrinker entropy

Huai-Dong Cao Lehigh University Meng Zhu ECNU, China & UC Riverside

Differential Geometry mathscidoc:1703.10007

Math. Ann., 353, (3), 747–763, 2012
In this paper we provide a detailed proof of the second variation formula, essentially due to Richard Hamilton, Tom Ilmanen and the first author, for Perelman’s ν-entropy. In particular, we correct an error in the stability operator stated in Theorem 6.3 of [2]. Moreover, we obtain a necessary condition for linearly stable shrinkers in terms of the least eigenvalue and its multiplicity of certain Lichnerowicz type operator associated to the second variation.
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@inproceedings{huai-dong2012on,
  title={On second variation of Perelman's Ricci shrinker entropy},
  author={Huai-Dong Cao, and Meng Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170313111442193255665},
  booktitle={Math. Ann.},
  volume={353},
  number={3},
  pages={747–763},
  year={2012},
}
Huai-Dong Cao, and Meng Zhu. On second variation of Perelman's Ricci shrinker entropy. 2012. Vol. 353. In Math. Ann.. pp.747–763. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170313111442193255665.
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