As on arXiv
Abstract
For any 3D steady gradient Ricci soliton with positive curvature, we prove that it must be isometric to the Bryant soliton if it is asymptotic to a ray. Otherwise, it is asymptotic to a sector and hence a flying wing. We show that all 3D flying wings are O(2)-symmetric. Therefore, all 3D steady gradient Ricci solitons are O(2)-symmetric.
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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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3D flying wings for any asymptotic cones
Topics 3-manifolds, Ricci solitons · Same author Yi Lai · Shared terms “flying wing”, “steady gradient”, “gradient Ricci”
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A family of Kähler flying wing steady Ricci solitons
Topics Ancient solutions, Ricci solitons · Same author Yi Lai · Shared terms “flying wing”, “steady gradient”, “positive curvature”
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Higher-dimensional flying wing Steady Ricci Solitons
Topics Ricci solitons · Same author Yi Lai · Shared terms “flying wing”, “steady gradient”, “gradient Ricci”
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Steady Gradient Ricci Solitons with Symmetry
Topics Ricci solitons · Shared terms “steady gradient”, “gradient Ricci”, “positive curvature”
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Rigidity of positively curved Steady gradient Ricci solitons on orbifolds
Topics Ancient solutions, Ricci solitons · Shared terms “steady gradient”, “gradient Ricci”, “Bryant soliton”
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Unique Asymptotics of Steady Ricci Solitons with Symmetry
Topics Ancient solutions, 3-manifolds, Ricci solitons
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An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons
Topics Ancient solutions, Ricci solitons · Shared terms “steady gradient”, “gradient Ricci”, “Bryant soliton”
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A comparison theorem for steady Ricci solitons
Topics Ancient solutions, Ricci solitons · Shared terms “Bryant soliton”, “steady 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
- 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.
- 11B.2Ancient Solutions and the Harnack Inequality
Comparing curvature across space and time.
- 12B.1κ-Solutions
Ancient, nonnegatively curved, noncollapsed: the models for singularities.