As on arXiv
Abstract
This paper studies a complete gradient Ricci soliton with an isoparametric potential function. Our first theorem asserts that, for the steady case, there is a critical level set of codimension greater than one. This is consistent with construction of cohomogeneity one models with singular orbits. There is a partial result for the shrinking case. We also study a particular ansatz of popular interest and obtain asymptotic behaviors.
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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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Steady conformally Kähler Ricci solitons with isoparametric potential
Topics Homogeneous spaces, Ricci solitons · Same author Hung Tran · Shared terms “isoparametric potential”, “potential function”, “cohomogeneity”
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Kähler Solitons, Contact Structures, and Isoparametric Functions
Topics Homogeneous spaces, Ricci solitons · Same author Hung Tran · Shared terms “isoparametric”, “potential function”, “cohomogeneity”
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Kähler-Ricci solitons with almost maximal symmetry
Topics Homogeneous spaces, Ricci solitons · Same author Hung Tran · Shared terms “potential function”, “cohomogeneity”, “gradient Ricci”
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Classification of superpotentials for cohomogeneity one Ricci solitons
Topics Homogeneous spaces, Ricci solitons · Shared terms “cohomogeneity”, “gradient Ricci”
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Kähler Soliton Surfaces Are Generically Toric
Topics Ricci solitons · Same author Hung Tran · Shared terms “potential function”, “gradient Ricci”
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Inhomogeneous deformations of Einstein solvmanifolds
Topics Homogeneous spaces, Ricci solitons · Shared terms “cohomogeneity”, “gradient Ricci”
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Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals
Topics Homogeneous spaces · Same author Hung Tran · Shared terms “level set”
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Geometry and Analysis of Gradient Ricci Solitons in Dimension Four
Topics Ricci solitons · Same author Hung Tran · Shared terms “gradient Ricci”, “asymptotic behavior”
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
- 11A.13Homogeneous Flows
A computable laboratory: the flow on Thurston’s geometries.
- 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.