Paper · Nov 10, 2022
Self-expanders to the mean curvature flow based on the generalized Lawson-Osserman cone
As on arXiv
Abstract
We derive the equation of self-similar solutions to mean curvature flow based on the generalized Lawson-Osserman cone and prove the existence of self-expanders by modifying the theory of equilibria in the autonomous system. In particular, those self-expanders are unique if a local assumption is given.
- Submitted
- Nov 10, 2022
- Last revised
- Feb 15, 2023 (v2)
- Subjects
- math.DG, math.CA
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.
-
On knotted self expanders of the mean curvature flow in
Topics Self-shrinkers & translators · Shared terms “self expanders”
-
Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow
Topics Self-shrinkers & translators · Shared terms “self expanders”
-
Self-expanders of positive genus
Topics Self-shrinkers & translators · Shared terms “self expanders”
-
Poincaré inequality and topological rigidity of translators and self-expanders for the mean curvature flow
Topics Self-shrinkers & translators · Shared terms “self expanders”
-
Entire self-expanders for power of curvature flow in Minkowski space
Topics Self-shrinkers & translators · Shared terms “self expanders”
-
The rigidity theorems for complete self-expander of mean curvature flow
Topics Self-shrinkers & translators · Shared terms “self expanders”
-
No breather theorems for the mean curvature flow
Topics Self-shrinkers & translators · Shared terms “self expanders”
-
The global structure of bi-rotational self-expanders
Topics Self-shrinkers & translators · Shared terms “self expanders”
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
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.