Paper · Oct 7, 2025
On curvature estimates for four-dimensional gradient Ricci solitons
As on arXiv
Abstract
In this survey paper, we analyse and compare the recent curvature estimates for three types of -dimensional gradient Ricci solitons, especially between Ricci shrinkers [58] and expanders [17]. In addition, we provide some new curvature estimates for -dimensional gradient steady Ricci solitons, including the sharp curvature estimate for gradient steady Ricci solitons with positive Ricci curvature (see Theorem 1.1).
Comments: 32 pages
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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
- 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.