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arXiv · 1008.0842

On second variation of Perelman's Ricci shrinker entropy

Huai-Dong Cao·Meng Zhu
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Abstract

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 [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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Huai-Dong Cao, Meng Zhu. 2010-08-04. On second variation of Perelman's Ricci shrinker entropy. https://arxiv.org/abs/1008.0842

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