Rigidity and gap theorems for Ricci shrinkers

Pak-Yeung Chan; Yongjia Zhang

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arXiv · 2605.08884

Rigidity and gap theorems for Ricci shrinkers

Pak-Yeung Chan·Yongjia Zhang

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Abstract

We prove local versions of the Ricci curvature and $\nu$-entropy gap theorems for Ricci shrinkers, which respectively generalize a previous result of Munteanu-Wang and a prior result of the authors with Ma. The key point is that these local gaps depend only on the dimension and not on the global entropy or any other geometric information of the Ricci shrinker. As an application, we provide a local criterion for removable Type~I singularities of the Ricci flow.

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BibTeX RIS

Pak-Yeung Chan, Yongjia Zhang. 2026-05-09. Rigidity and gap theorems for Ricci shrinkers. https://arxiv.org/abs/2605.08884

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