On second variation of Perelman’s Ricci shrinker entropy

By Huaihuo Cao, Meng Zhu. Mathematische Annalen, 2010

72 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7461cee0fa20151ac0c3ce052c27624e7e82444c

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In Applied Mathematics

1. Chenxu He
2. Huaihuo Cao
3. Qiang Chen
4. Ovidiu Munteanu
5. Jiaping Wang
6. Brett Kotschwar
7. Lu Wang
8. G. Catino

In Geometry and Topology

1. Chenxu He
2. Huaihuo Cao
3. Qiang Chen
4. Ovidiu Munteanu
5. Jiaping Wang
6. Lu Wang
7. Brett Kotschwar
8. G. Catino

Citations in the corpus

• Linear stability of Perelman's $ν$-entropy on symmetric spaces of compact type (2013, background): “nique solution of ∆vh + vh 2τ = divdivh. Remark 3.2. (1) The details of the calculation of the second variation formula at a general shrinking Ricci soliton are given by the first author and M. Zhu in [CZ] which includes the above formula as a special case. (2) Note that the uniqueness of vh follows ”