As on arXiv
Abstract
We prove that a complete solution to the Ricci flow on which has quadratic curvature decay on some end of and converges locally smoothly to the end of a cone on that neighborhood as must be a gradient shrinking soliton.
Comments: 52 pages, no figures
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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Backward propagation of warped product structures and asymptotically conical shrinkers
Topics Ricci solitons · Same author Brett Kotschwar · Shared terms “shrinking solitons”, “gradient shrinking”
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Uniqueness of Asymptotically Conical Gradient Shrinking Solitons in G_2-Laplacian Flow
Topics Ricci solitons · Shared terms “shrinking solitons”, “gradient shrinking”
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Uniqueness of asymptotically conical Kähler-Ricci flow
Topics Ricci solitons · Shared terms “complete solution”, “quadratic curvature”, “curvature decay”
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On the shrinking solitons of generalized Ricci flow
Topics Ricci solitons · Shared terms “shrinking solitons”, “gradient shrinking”
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Ricci solitons as critical points of quadratic curvature functionals
Topics Ricci solitons · Shared terms “quadratic curvature”
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On a dichotomy of the curvature decay of steady Ricci soliton
Topics Ricci solitons · Shared terms “curvature decay”
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Rigidity of Gradient Shrinking Ricci Solitons with a Vanishing Bach-like Tensor and Related Variational Formulas
Topics Ricci solitons · Shared terms “gradient shrinking”, “quadratic curvature”
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Ends of (singular) Ricci shrinkers
Topics Ricci solitons
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.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.
- 12B.2The Asymptotic Soliton and Three-Dimensional Shrinkers
Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.
- 5A.5Uniformization and the Two-Dimensional Ricci Flow
Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.