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

来源：

MATHEMATISCHE ANNALEN | 2012年 / 353卷 / 03期

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

页码：747 / 763

页数：17

共 17 条

[11]

Hamilton R.S., 1988, MATH GEN RELATIVITY, V71, P237

[12] RICCI SOLITONS ON COMPACT 3-MANIFOLDS [J].