As on arXiv
Abstract
We show that the normalized Kähler-Ricci flow on a compact Kähler manifold with semiample canonical bundle converges in the Gromov-Hausdorff topology to the metric completion of the twisted Kähler-Einstein metric on the canonical model, as conjectured by Song-Tian's analytic mimimal model program.
Comments: 35 pages; fixed a gap and typos
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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Collapsing immortal Kähler-Ricci flows
Topics Analytic minimal model program, Kähler–Ricci flow, Long-time existence & convergence · Same authors Man-Chun Lee, Valentino Tosatti · Shared terms “immortal kahler”, “semiample canonical”, “canonical bundle”
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Gromov-Hausdorff Convergence of Constant Scalar Curvature Kähler Metrics near the Canonical Class
Topics Analytic minimal model program, Kähler–Einstein & K-stability, Kähler–Ricci flow · Shared terms “Gromov Hausdorff”, “canonical model”, “metric completion”
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Immortal solutions of the Kähler-Ricci flow
Topics Kähler–Ricci flow, Long-time existence & convergence, Kähler geometry · Same author Valentino Tosatti · Shared terms “immortal”, “compact Kähler”
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Gromov-Hausdorff Limits of Noncollapsed Kähler-Ricci Flows and the Geometry of Ricci Shrinkers
Topics Kähler–Ricci flow, Limit spaces & RCD, Kähler geometry · Same author Junsheng Zhang · Shared terms “Hausdorff limit”, “Gromov Hausdorff”, “completion”
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Convergence of Scalar Curvature of Long Time Kähler-Ricci Flow on Kähler Manifold
Topics Analytic minimal model program, Kähler–Ricci flow, Kähler geometry · Shared terms “normalized Kähler”, “semiample canonical”, “canonical bundle”
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Fano Fibrations and Twisted Kähler-Einstein Metrics I
Topics Analytic minimal model program, Kähler–Einstein & K-stability, Kähler–Ricci flow · Shared terms “twisted Kähler”, “compact Kähler”
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Higher-order Ricci estimates along immortal Kähler-Ricci flows
Topics Analytic minimal model program, Kähler–Ricci flow, Long-time existence & convergence · Shared terms “immortal kahler”, “compact Kähler”
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Fano Fibrations and Twisted Kähler-Einstein Metrics II: The Kähler-Ricci Flow
Topics Analytic minimal model program, Kähler–Einstein & K-stability, Kähler–Ricci flow · Shared terms “twisted Kähler”, “compact Kähler”
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
- 5A.6Where This Track Leads
The Kähler–Ricci flow, and when to come back to it.
- 6C.11Optimal Transport and Ricci Curvature
Kantorovich duality, Wasserstein geometry, the heat equation as a gradient flow of entropy, displacement convexity, and Ricci curvature as convexity, from Lott–Sturm–Villani to McCann–Topping and the reduced volume.
- 9B.4Convergence of Manifolds
Gromov–Hausdorff and Cheeger–Gromov convergence, and the compactness theorem.