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On noncollapsed $\mathbb{F}$-limit metric solitons
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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.
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Cited by 2 Pith papers
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Remarks on Singular K\"ahler-Einstein Metrics
Rough singular Kähler-Einstein metrics, when the metric completion is an RCD space, are equivalent to the Eyssidieux-Guedj-Zeriahi notion and imply log terminal singularities; this applies to tangent cones of noncolla...
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On the structure of noncollapsed Ricci flow limit spaces
Ricci flow limit spaces under bounded entropy have regular parts that form Ricci flow spacetimes and singular sets of codimension at least four.
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