Paper · Jun 22, 2022
A new complete two-dimensional shrinking gradient Kähler-Ricci soliton
As on arXiv
Abstract
We prove the existence of a unique complete shrinking gradient Kähler-Ricci soliton with bounded scalar curvature on the blowup of at one point. This completes the classification of such solitons in two complex dimensions.
Comments: 11 pages
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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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Uniqueness of the soliton vector field of a shrinking gradient Kähler-Ricci soliton
Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Same authors Ronan J. Conlon, Alix Deruelle · Shared terms “shrinking gradient”, “gradient Kähler”, “complete shrinking”
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Uniqueness of shrinking Kähler-Ricci solitons on resolutions of Kähler cones
Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Same authors Ronan J. Conlon, Alix Deruelle · Shared terms “shrinking gradient”, “gradient Kähler”, “complete shrinking”
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On finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces
Topics Kähler–Ricci solitons, Scalar curvature, Kähler geometry · Same authors Charles Cifarelli, Ronan J. Conlon, Alix Deruelle · Shared terms “dimensional shrinking”, “shrinking gradient”, “gradient Kähler”
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An Aubin continuity path for shrinking gradient Kähler-Ricci solitons
Topics Kähler–Ricci solitons, Kähler geometry, Singularities · Same authors Charles Cifarelli, Ronan J. Conlon, Alix Deruelle · Shared terms “shrinking gradient”, “gradient Kähler”
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An Aubin continuity path for asymptotically conical toric shrinking gradient Kähler-Ricci solitons: openness and a solution for
Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Same authors Ronan J. Conlon, Alix Deruelle · Shared terms “shrinking gradient”, “gradient Kähler”
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A non-Kähler expanding Ricci soliton with a Kähler tangent cone at infinity
Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Same authors Richard H. Bamler, Ronan J. Conlon · Shared terms “gradient Kähler”
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Shrinking gradient Kähler-Ricci solitons are simply-connected
Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “shrinking gradient”, “gradient Kähler”
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Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature
Topics Scalar curvature, Ricci solitons · Shared terms “dimensional shrinking”, “shrinking gradient”
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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
- 5A.5Uniformization and the Two-Dimensional Ricci Flow
Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.
- 11A.12Ricci Flow on Surfaces
Uniformization by Ricci flow, and Hamilton’s entropy.
- 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.