On second variation of Perelman's Ricci shrinker entropy

被引:41
作者
Cao, Huai-Dong [1 ]
Zhu, Meng [1 ]
机构
[1] Lehigh Univ, Dept Math, Bethlehem, PA 18015 USA
基金
美国国家科学基金会;
关键词
SOLITONS;
D O I
10.1007/s00208-011-0701-0
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
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 nu-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.
引用
收藏
页码:747 / 763
页数:17
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