As on arXiv
Abstract
We will show that if a gradient shrinking Ricci soliton has an approximate symmetry on one scale, this symmetry propagates to larger scales. This is an example of the shrinker principle which roughly states that information radiates outwards for shrinking solitons.
Its neighbourhood
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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Singularities of Ricci flow and diffeomorphisms
Topics Ricci solitons · Same authors Tobias Holck Colding, William P. Minicozzi · Shared terms “shrinker principle”, “propagation”
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A strong Frankel Theorem for shrinkers
Topics Ricci solitons · Same authors Tobias Holck Colding, William P. Minicozzi
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Optimal growth bounds for eigenfunctions
Topics Ricci solitons · Same authors Tobias Holck Colding, William P. Minicozzi · Shared terms “propagation”, “approximate”
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Singularities and diffeomorphisms
Same authors Tobias Holck Colding, William P. Minicozzi
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Eigenvalue lower bounds and splitting for modified Ricci flow
Same authors Tobias Holck Colding, William P. Minicozzi
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Distance between minimal surfaces and flows
Same authors Tobias Holck Colding, William P. Minicozzi · Shared terms “information”
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Quantitative uniqueness for mean curvature flow
Same authors Tobias Holck Colding, William P. Minicozzi
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Backward propagation of warped product structures and asymptotically conical shrinkers
Topics Ricci solitons · Shared terms “propagation”, “propagates”, “shrinking solitons”
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.