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Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers

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arxiv 2202.03386 v2 pith:XVMDTL2V submitted 2022-02-07 math.DG math.AP

Maxwell Stolarski This is my paper · ORCID
classification math.DGmath.AP
keywords riccisolitonasymptoticallyclosedconicalgivenmodeledsingularity
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Given an asymptotically conical, shrinking, gradient Ricci soliton, we show that there exists a Ricci flow solution on a closed manifold that forms a finite-time singularity modeled on the given soliton. No symmetry or Kahler assumptions on the soliton are required. The proof provides a precise asymptotic description of the singularity formation.

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Cited by 1 Pith paper

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  1. The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow

    math.DG 2025-06 conditional novelty 8.0 of 10

    Every immersed 2-sphere with Willmore energy at most 12π admits an energy-nonincreasing regular homotopy to a round sphere or to a surface in the explicit family J, giving exactly four regular homotopy classes below 12π.

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