As on arXiv
Abstract
We construct an embedded ancient solution to the mean curvature flow which is qualitatively given by a "stack" of two ancient pancakes joined by a neck. Our solution is closed, non-convex, and contained in a slab.
Comments: Introduction expanded and figure added, along with some other clarifications and improvements. Comments welcome!
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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Ancient pancake solutions to fully nonlinear curvature flows
Topics Ancient solutions · Shared terms “pancake solution”, “ancient pancakes”
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A Bernstein theorem of ancient solutions to mean curvature flow
Topics Ancient solutions
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Ancient Gauss Curvature Flows of Bounded Width
Topics Ancient solutions · Shared terms “contained”
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A Bernstein theorem for ancient solution to symplectic mean curvature flow
Topics Ancient solutions
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Nonplanar ancient curve shortening flows in from grim reapers
Topics Ancient solutions · Same author Alexander Mramor
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A rigidity theorem of ancient solutions to the mean curvature flow in codimension one
Topics Ancient solutions
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Mean curvature flows with prescribed singular sets
Topics Ancient solutions
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.2Ancient Solutions and the Harnack Inequality
Comparing curvature across space and time.
- 12B.1κ-Solutions
Ancient, nonnegatively curved, noncollapsed: the models for singularities.
- 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.