As on arXiv
Abstract
We prove that every complete Kähler–Ricci shrinker with nonnegative Ricci curvature is holomorphically isometric to for some , where is the Gaussian shrinker and is a compact Kähler–Ricci shrinker with nonnegative Ricci curvature. As a corollary, every complete Kähler–Ricci shrinker with quasi-positive Ricci curvature is compact.
Comments: 14 pages. 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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Compactness and Rigidity of Complete Kähler Ricci Shrinkers
Topics Kähler geometry, Ricci solitons · Same authors Tongxin Xu, Zhenlei Zhang · Shared terms “complete Kähler”, “Ricci shrinkers”
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Finite Time Type I Singularities of the Kähler Ricci Flow
Topics Kähler geometry, Ricci solitons · Same authors Tongxin Xu, Zhenlei Zhang · Shared terms “compact Kähler”
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Finite Time Singularities of Collapsing Kähler Ricci Flow on Ruled Surfaces
Topics Kähler geometry, Ricci solitons · Same authors Tongxin Xu, Zhenlei Zhang
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Collapsed Finite Time Singularities of the Kähler-Ricci Flow on Complex Surfaces are of Type I
Topics Kähler geometry · Same authors Tongxin Xu, Zhenlei Zhang · Shared terms “compact Kähler”
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On Kähler Ricci shrinker surfaces
Topics Kähler geometry, Ricci solitons · Shared terms “Ricci shrinkers”
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Uniqueness of Kähler Ricci shrinkers on toric orbifolds
Topics Kähler geometry, Ricci solitons · Shared terms “Ricci shrinkers”
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Some uniform estimates for Kähler–Ricci Shrinkers
Topics Kähler geometry, Ricci solitons · Shared terms “Ricci shrinkers”, “Gaussian shrinker”
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Convergence of Scalar Curvature of Long Time Kähler-Ricci Flow on Kähler Manifold
Topics Kähler geometry · Same author Zhenlei Zhang · Shared terms “compact Kähler”
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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.