As on arXiv
Abstract
In this paper, we survey the volume growth estimates for shrinking, steady, and expanding gradient Ricci solitons. Together with the known results, we also prove some new volume growth estimates for expanding gradient Ricci solitons.
Comments: 20 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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An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons
Topics Ricci solitons · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang · Shared terms “growth estimate”, “volume growth”, “gradient Ricci”
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Hamilton-Ivey estimates for gradient Ricci solitons
Topics Ricci solitons · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang · Shared terms “gradient Ricci”, “expanding gradient”
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On noncollapsed -limit metric solitons
Topics Ricci solitons · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang · Shared terms “volume growth”
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On the weakly conical expanding gradient Ricci solitons
Topics Ricci solitons · Same author Pak-Yeung Chan · Shared terms “expanding gradient”, “gradient Ricci”
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Dimension Reduction for Positively Curved Steady Solitons
Topics Ricci solitons · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang · Shared terms “gradient Ricci”
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Expanding Ricci solitons coming out of weakly PIC1 metric cones
Topics Ricci solitons · Same author Pak-Yeung Chan · Shared terms “volume growth”, “expanding gradient”, “gradient Ricci”
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A local gap theorem for Ricci shrinkers
Topics Ricci solitons · Same authors Pak-Yeung Chan, Zilu Ma, Yongjia Zhang
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Rigidity and gap theorems for Ricci shrinkers
Topics Ricci solitons · Same authors Pak-Yeung Chan, Yongjia Zhang
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
- 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.