As on arXiv
Abstract
We prove that a smooth toric Fano fibration admits a complete gradient shrinking Kähler-Ricci soliton.
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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Shrinking gradient Kähler-Ricci solitons are simply-connected
Topics Analytic minimal model program, Kähler–Ricci solitons, Kähler geometry · Shared terms “shrinking Kähler”, “Fano fibration”
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On Sun-Zhang's theory of Fano fibrations – weighted volumes, moduli and bubbling Fano fibrations
Topics Analytic minimal model program, Kähler–Ricci solitons, Kähler geometry · Shared terms “Fano fibration”
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Convergence of Generalized Kähler–Ricci Flow on Toric Fano Manifolds
Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “toric Fano”
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On a general class of free boundary Monge-Ampère equations
Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Same author Tristan C. Collins · Shared terms “toric Fano”
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On Kähler-Einstein Currents
Topics Analytic minimal model program, Kähler–Ricci solitons, Kähler geometry · Same author Freid Tong
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Singular Kähler–Ricci shrinkers and polarized Fano fibrations
Topics Analytic minimal model program, Kähler geometry, Ricci solitons · Shared terms “Fano fibration”
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Uniqueness of asymptotically conical shrinking gradient Kähler-Ricci solitons
Topics Analytic minimal model program, Kähler–Ricci solitons, Kähler geometry · Shared terms “Fano fibration”
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Compactness and Rigidity of Complete Kähler Ricci Shrinkers
Topics Analytic minimal model program, Kähler geometry, Ricci solitons · Shared terms “Fano fibration”
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.