On second variation of Perelman's Ricci shrinker entropy

Huai Dong Cao; Meng Zhu

doi:10.1007/s00208-011-0701-0

On second variation of Perelman's Ricci shrinker entropy

Huai Dong Cao^*
, Meng Zhu

^*此作品的通讯作者

Lehigh University

科研成果: 期刊稿件 › 文章 › 同行评审

43 引用（Scopus）

摘要

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 (Cao in Adv Lect Math 11:1-38, 2010). 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.

源语言	英语
页（从-至）	747-763
页数	17
期刊	Mathematische Annalen
卷	353
期	3
DOI	https://doi.org/10.1007/s00208-011-0701-0
出版状态	已出版 - 7月 2012
已对外发布	是

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AB - 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 (Cao in Adv Lect Math 11:1-38, 2010). 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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On second variation of Perelman's Ricci shrinker entropy

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