As on arXiv
Abstract
In this work, we construct several sequences of metrics on sphere with different limiting behaviors. By combining with the work of Deruelle, we use it and the localized maximum principle to construct various examples of expanding gradient Ricci solitons with positive curvature and exotic curvature decay. This answers a question proposed by Chow-Lu-Ni and also a question by Cao-Liu, respectively.
Comments: 18 pages. All comments are welcome
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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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Expanding Ricci solitons coming out of weakly PIC1 metric cones
Topics Ricci solitons · Same authors Pak-Yeung Chan, Man-Chun Lee · Shared terms “expanding gradient”, “gradient Ricci”, “Deruelle”
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Higher-dimensional flying wing Steady Ricci Solitons
Topics Ricci solitons · Same authors Pak-Yeung Chan, Man-Chun Lee · Shared terms “conical expanding”, “gradient Ricci”, “Deruelle”
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Curvature estimates for steady and expanding solitons in higher dimensions
Topics Ricci solitons · Same author Pak-Yeung Chan · Shared terms “Cao Liu”, “expanding gradient”, “curvature decay”
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Volume growth estimates of gradient Ricci solitons
Topics Ricci solitons · Same author Pak-Yeung Chan · Shared terms “expanding gradient”, “gradient Ricci”
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Gap Theorem on Riemannian manifolds using Ricci flow
Same authors Pak-Yeung Chan, Man-Chun Lee · Shared terms “curvature decay”, “combining”
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Hamilton-Ivey estimates for gradient Ricci solitons
Topics Ricci solitons · Same author Pak-Yeung Chan · Shared terms “expanding gradient”, “gradient Ricci”, “positive curvature”
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Manifolds with small curvature concentration
Same authors Pak-Yeung Chan, Man-Chun Lee
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A non-Kähler expanding Ricci soliton with a Kähler tangent cone at infinity
Topics Ricci solitons · Shared terms “expanding gradient”, “gradient Ricci”
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.