Paper · Oct 30, 2017
Complete Ricci solitons via estimates on the soliton potential
As on arXiv
Abstract
In this paper a growth estimate on the soliton potential is shown for a large class of cohomogeneity one manifolds. This is used to construct continuous families of complete steady and expanding Ricci solitons in the set-ups of Lü-Page-Pope and Dancer-Wang. It also provides a different approach to the two summands system which applies to all known geometric examples.
- Submitted
- Oct 30, 2017
- Last revised
- Oct 28, 2019 (v2)
- Subjects
- math.DG
- Journal
- Int. Math. Res. Not. IMRN (2021), no. 6, 4487-4521
Comments: 22 pages
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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.