Paper · Apr 26, 2019
A family of MCF solutions for the Heisenberg Group
As on arXiv
Abstract
The aim of this paper is to investigate the mean curvature flow soliton solutions on the Heisenberg group when the initial data is a ruled surface by straight lines. We give a family of those solutions which are generated by (the isometries of for which the origin is a fix point). We conclude that the function which describe the motion of these surfaces under MCF, is always a linear affine function. As an application we proof that the Grim Reaper solution evolves from a ruled surface in . We also provide other examples.
- Submitted
- Apr 26, 2019
- Subjects
- math.DG
- Journal
- Differential Geometry and its Applications 2020
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 2016, plus the canon.
-
Self-similar solutions to the mean curvature flow in
Topics Mean curvature flow · Same author Benedito Leandro · Shared terms “MCF”, “ruled surfaces”
-
Ruled surfaces of generalized self-similar solutions of the mean curvature flow
Topics Self-shrinkers & translators · Shared terms “ruled surfaces”
-
Invariant translators of the Heisenberg group
Topics Self-shrinkers & translators · Shared terms “Heisenberg group”, “grim reaper”, “isometry”
-
Invariant -translators in the Heisenberg group
Topics Self-shrinkers & translators · Shared terms “Heisenberg group”, “isometry”
-
Ruled surfaces as translating solitons of the inverse mean curvature flow in the three-dimensional Lorentz-Minkowski space
Topics Self-shrinkers & translators · Shared terms “ruled surfaces”
-
The class of grim reapers in
Topics Self-shrinkers & translators · Shared terms “grim reaper”
-
Translators to Higher Order Mean Curvature Flows in and
Topics Self-shrinkers & translators · Shared terms “MCF”, “grim reaper”
-
Solitons to Mean Curvature Flow in the hyperbolic 3-space
Topics Self-shrinkers & translators · Shared terms “MCF”
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.