As on arXiv
Abstract
In this paper, we prove that any Kähler Ricci shrinker surface has bounded sectional curvature. Combining this estimate with earlier work by many authors, we provide a complete classification of all Kähler Ricci shrinker surfaces.
Comments: 43 pages, 3 figures, 1 table; Revised version, to appear in Acta Mathematica
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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Uniqueness of Kähler Ricci shrinkers on toric orbifolds
Topics Kähler geometry, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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Rigidity of the round cylinders in Ricci shrinkers
Topics Ricci solitons · Same authors Yu Li, Bing Wang · Shared terms “Ricci shrinkers”
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Heat kernel on Ricci shrinkers (II)
Topics Ricci solitons · Same authors Yu Li, Bing Wang · Shared terms “Ricci shrinkers”
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Scalar curvature bounds and tangent cones for Kähler–Ricci shrinkers
Topics Kähler geometry, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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Kähler-Ricci Shrinkers with Nonnegative Ricci Curvature
Topics Kähler geometry, Ricci solitons · Shared terms “Ricci shrinkers”
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Rigidity of complex projective spaces in Ricci shrinkers
Topics Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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Non-collapsing of Ricci shrinkers with bounded curvature
Topics Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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Gromov-Hausdorff Limits of Noncollapsed Kähler-Ricci Flows and the Geometry of Ricci Shrinkers
Topics Kähler geometry, Ricci solitons · Same author Yu Li · Shared terms “Ricci shrinkers”
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.