Work

On noncollapsed $\mathbb{F}$-limit metric solitons

Year: 2024

Type: preprint

Abstract: A noncollapsed $\mathbb{F}$-limit metric soliton is a self-similar singularity model that inevitably arises when studying the Ricci flow with the tool of $\mathbb{F}$-convergence [Bam20a,Bam20b,Bam20c]. In this article, we shall present a systematic study of the noncollapsed $\mathbb{F}$-limit metric soliton, and show that, apart from the known results in [Bam20c], it satisfies many properties of smooth Ricci shrinkers. In particular, we show a quadratic lower bound for the scalar curvature, a local gap theorem, a global Sobolev inequality, and an optimal volume growth lower bound.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2401.03387

Authors: Chan, Pak-Yeung, Ma, Zilu, Zhang, Yongjia

Institutions: Rutgers, The State University of New Jersey, Shanghai Jiao Tong University, University of Warwick

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Engineering and Physical Sciences Research Council

Awards: Ricci flow of manifolds with singularities at infinity, G2491852346

OpenAlex ID: W4390722944

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