Paper · Oct 8, 2025
Stability of asymptotically conical gradient Kähler-Ricci expanders
As on arXiv
Abstract
In this work, we consider a perturbation of an asymptotically conical gradient expanding Kähler-Ricci soliton metric in the same Kähler class. We demonstrate that, under suitable assumptions, the normalized Kähler-Ricci flow starting from the initial perturbed metric exists for all time and converges uniformly to an asymptotically conical gradient expanding Kähler-Ricci soliton metric . Moreover, if the perturbed initial metric is asymptotic to at spatial infinity, then the limiting metric coincides with the original soliton, that is, .
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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
- 5A.6Where This Track Leads
The Kähler–Ricci flow, and when to come back to it.
- 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.