As on arXiv
Abstract
We consider the graphical mean curvature flow of maps , , and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed submanifolds that extends the well-known maximum principle of Ecker and Huisken derived in their seminal paper [10]. In the case of uniformly area decreasing maps , , we use this maximum principle to show that the graphicality and the area decreasing property are preserved. Moreover, if the initial graph is asymptotically conical at infinity, we prove that the normalized mean curvature flow smoothly converges to a self-expander.
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.
-
Graphical mean curvature flow with bounded bi-Ricci curvature
Topics Mean curvature flow · Same authors Andreas Savas-Halilaj, Knut Smoczyk · Shared terms “area decreasing”, “graphical mean”, “decreasing maps”
-
Convexity of mean convex asymptotically conical self-expanders to the mean curvature flow
Topics Self-shrinkers & translators, Boundaries & non-compact · Shared terms “self expanders”, “asymptotically conical”
-
No breather theorems for the mean curvature flow
Topics Self-shrinkers & translators, Boundaries & non-compact · Shared terms “self expanders”
-
The Boundary Term in Huisken's Monotonicity Formula and the Entropy of Translators
Topics Self-shrinkers & translators, Boundaries & non-compact · Shared terms “Huisken”
-
Sharp Interior Gradient Estimate for Area Decreasing Graphical Mean Curvature Flow in Arbitrary Codimension
Topics Mean curvature flow · Shared terms “area decreasing”, “graphical mean”
-
Backwards uniqueness for Mean curvature flow with asymptotically conical singularities
Topics Self-shrinkers & translators, Boundaries & non-compact · Shared terms “asymptotically conical”
-
Conformal solitons for the mean curvature flow in hyperbolic space
Topics Self-shrinkers & translators, Boundaries & non-compact · Same author Andreas Savas-Halilaj · Shared terms “expander”
-
Self-expanders to the mean curvature flow based on the generalized Lawson-Osserman cone
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.