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arXiv · 2611.07381

Scalar curvature bounds and rigidity of Ricci shrinkers

Jianyu Ou·Guoqiang Wu
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Abstract

We prove that a complete noncompact gradient shrinking Ricci soliton of dimension at least two is a finite quotient of an Einstein cylinder if its scalar curvature is bounded below by the cylindrical value. The corresponding pointwise strict bound implies compactness. We also establish one-endedness criteria using curvature information at critical points of the potential, including degenerate ones, and obtain sharp one-endedness and rigidity results under global Ricci norm bounds.

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Jianyu Ou, Guoqiang Wu. 2026-11-05. Scalar curvature bounds and rigidity of Ricci shrinkers. https://arxiv.org/abs/2611.07381

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