As on arXiv
Abstract
In this paper, we establish several uniform estimates for Kähler–Ricci shrinkers without imposing any curvature assumptions. In particular, we prove: 1. a uniform lower bound for the entropy; 2. a uniform lower bound for the asymptotic volume ratio of Kähler–shrinkers with maximal volume growth; 3. a uniform lower bound for the scalar curvature on balls centered at a minimum point of the soliton potential for non-Gaussian shrinkers.
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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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Scalar curvature bounds and tangent cones for Kähler–Ricci shrinkers
Topics Scalar curvature, Kähler geometry, Ricci solitons · Same author Junsheng Zhang · Shared terms “Ricci shrinkers”, “maximal volume”, “volume growth”
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Gromov-Hausdorff Limits of Noncollapsed Kähler-Ricci Flows and the Geometry of Ricci Shrinkers
Topics Scalar curvature, Kähler geometry, Ricci solitons · Same author Junsheng Zhang · Shared terms “Ricci shrinkers”, “volume growth”
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Weak transcendental base-point freeness and diameter lower bounds for the Kähler-Ricci flow
Topics Kähler geometry · Same author Junsheng Zhang · Shared terms “lower bound”
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On Kähler Ricci shrinker surfaces
Topics Kähler geometry, Ricci solitons · Shared terms “Ricci shrinkers”
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Kähler-Ricci shrinkers and Fano fibrations
Topics Kähler geometry, Ricci solitons · Same author Junsheng Zhang · Shared terms “Ricci shrinkers”
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A Matsushima theorem, uniqueness and K-polystability for Kähler-Ricci shrinkers
Topics Kähler geometry, Ricci solitons · Same author Junsheng Zhang · Shared terms “Ricci shrinkers”
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Singular Kähler–Ricci shrinkers and polarized Fano fibrations
Topics Kähler geometry, Ricci solitons · Same author Junsheng Zhang · Shared terms “Ricci shrinkers”
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Kähler-Ricci Shrinkers with Nonnegative Ricci Curvature
Topics Kähler geometry, Ricci solitons · Shared terms “Ricci shrinkers”, “Gaussian shrinker”
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
- 6C.4The Yamabe Problem and Critical Exponents
Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.
- 9B.6Scalar Curvature and Topology
Positive scalar curvature, its obstructions, and the positive mass theorem.
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.