As on arXiv
Abstract
For every closed set and every , we construct a mean-convex ancient solution to mean curvature flow of hypersurfaces in , with respect to a smooth Riemannian metric arbitrarily -close to the Euclidean metric, whose first-time singular set is exactly .
Comments: 19 pages
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.
-
Volume estimates for the singular sets of mean curvature flows
Topics Mean curvature flow · Shared terms “singular set”, “mean convex”
-
A Bernstein theorem of ancient solutions to mean curvature flow
Topics Ancient solutions
-
A Bernstein theorem for ancient solution to symplectic mean curvature flow
Topics Ancient solutions
-
An Ancient Stacked Pancake Solution to Mean Curvature Flow
Topics Ancient solutions
-
Mean Curvature Flow for Isoparametric Submanifolds in Hyperbolic Spaces
Topics Ancient solutions · Shared terms “Euclidean”
-
Generalized Harnack Inequality for Mean Curvature Flow and Ancient Solutions
Topics Ancient solutions · Shared terms “convex ancient”, “mean convex”
-
A rigidity theorem of ancient solutions to the mean curvature flow in codimension one
Topics Ancient solutions
-
Classification of convex ancient free boundary mean curvature flows in the ball
Topics Ancient solutions · Shared terms “convex ancient”
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.