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arXiv · 2208.13206

Lower bounds for the scalar curvatures of Ricci flow singularity models

Pak-Yeung Chan·Bennett Chow·Zilu Ma·Yongjia Zhang
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Abstract

In a series of papers, Bamler [Bam20a,Bam20b,Bam20c] further developed the high-dimensional theory of Hamilton's Ricci flow to include new monotonicity formulas, a completely general compactness theorem, and a long-sought partial regularity theory analogous to Cheeger--Colding theory. In this paper we give an application of his theory to lower bounds for the scalar curvatures of singularity models for Ricci flow. In the case of $4$-dimensional non-Ricci-flat steady soliton singularity models, we obtain as a consequence a quadratic decay lower bound for the scalar curvature.

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Pak-Yeung Chan, Bennett Chow, Zilu Ma, Yongjia Zhang. 2022-08-28. Lower bounds for the scalar curvatures of Ricci flow singularity models. https://arxiv.org/abs/2208.13206

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