As on arXiv
Abstract
In this paper we prove that there exists a compact perturbation of the Ricci flat Taub-Bolt metric that evolves under the Ricci flow into a finite time singularity modelled on the shrinking solition FIK [5]. Moreover, this perturbation can be made arbitrarily L^2-small with respect to the Taub-Bolt metric. The method of proof closely follows the strategy adopted in [14], where the author constructs, via a Ważewski box argument, Ricci flows on compact manifolds which encounter finite singularities modelled on a given asymptotically conical shrinking soliton.
Comments: arXiv admin note: text overlap with arXiv:2202.03386 by other authors
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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An ancient Ricci flow emerging from Taub-Bolt
Topics Ricci flow · Same author John Hughes · Shared terms “Taub Bolt”, “Bolt metric”
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Towards a Taub-Bolt to Taub-NUT via Ricci flow with surgery
Topics Singularities · Same author John Hughes · Shared terms “Taub Bolt”
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Topics Ricci-flat & Calabi–Yau, Boundaries & non-compact · Shared terms “instability”, “perturbation”
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Closed Ricci Flows with Singularities Modeled on Asymptotically Conical Shrinkers
Topics Boundaries & non-compact, Singularities, Ricci solitons · Shared terms “asymptotically conical”, “time singularity”, “finite time”
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Robinson-Trautman solutions with scalar hair and Ricci flow
Topics Ricci-flat & Calabi–Yau, Boundaries & non-compact, Singularities
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Closed mean curvature flows with asymptotically conical singularities
Topics Boundaries & non-compact, Singularities, Ricci solitons · Shared terms “box argument”, “Ważewski box”, “asymptotically conical”
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The asymptotic behavior of the steady gradient Kähler-Ricci soliton of the Taub-NUT type of Apostolov and Cifarelli
Topics Ricci-flat & Calabi–Yau, Ricci solitons · Shared terms “Taub”
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Uniqueness of asymptotically conical shrinking gradient Kähler-Ricci solitons
Topics Ricci-flat & Calabi–Yau, Boundaries & non-compact, Ricci solitons · Shared terms “conical shrinking”, “asymptotically conical”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.4Blow-Ups, Blow-Downs and Splitting at Infinity
Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.
- 11B.6Rotationally Symmetric Flows and the Standard Solution
The neckpinch in equations: warped products under the flow, what the maximum principle forces, and the standard solution that surgery glues in.
- 6A.13Self-Similar Variables and Monotonicity
Changing variables so that self-similar solutions stand still: convergence to the Gaussian, Giga–Kohn blow-up, Gaussian-weighted monotonicity formulas, frequency functions, and the blow-up logic of Huisken, Struwe and Perelman.