As on arXiv
Abstract
We prove a strong Frankel theorem for mean curvature flow shrinkers in all dimensions: Any two shrinkers in a sufficiently large ball must intersect. In particular, the shrinker itself must be connected in all large balls. The key to the proof is a strong Bernstein theorem for incomplete stable Gaussian surfaces.
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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Optimal growth bounds for eigenfunctions
Topics Ricci solitons · Same authors Tobias Holck Colding, William P. Minicozzi · Shared terms “Gaussian”
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Propagation of symmetries for Ricci shrinkers
Topics Ricci solitons · Same authors Tobias Holck Colding, William P. Minicozzi
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Singularities of Ricci flow and diffeomorphisms
Topics Ricci solitons · Same authors Tobias Holck Colding, William P. Minicozzi
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Distance between minimal surfaces and flows
Topics Mean curvature flow · Same authors Tobias Holck Colding, William P. Minicozzi
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Quantitative uniqueness for mean curvature flow
Topics Mean curvature flow · 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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Singularities and diffeomorphisms
Same authors Tobias Holck Colding, William P. Minicozzi
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A Bernstein theorem of ancient solutions to mean curvature flow
Topics Mean curvature flow · Shared terms “Bernstein theorem”
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.
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.