On the rigidity of Ricci shrinkers

Yu Li; Wenjia Zhang

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arXiv · 2305.06143

On the rigidity of Ricci shrinkers

Yu Li·Wenjia Zhang

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Abstract

In this paper, we establish the rigidity of the generalized cylinder $N^n \times \mathbb R^{m-n}$, or a quotient thereof, in the space of Ricci shrinkers equipped with the pointed-Gromov-Hausdorff topology. Here, $N$ is a stable Einstein manifold that has an obstruction of order $3$. The proof is based on a quantitative characterization of the rigidity of compact Ricci shrinkers, a rigidity inequality of mixed orders on generalized cylinders, and the method of contraction and extension. As an application, we prove the uniqueness of the tangent flow for general compact Ricci flows under the assumption that one tangent flow is a generalized cylinder.

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BibTeX RIS

Yu Li, Wenjia Zhang. 2025-01-02. On the rigidity of Ricci shrinkers. https://arxiv.org/abs/2305.06143

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