The Structure of Translating Surfaces with Finite Total Curvature

Ilyas Khan

The Structure of Translating Surfaces with Finite Total Curvature

Differential Geometry 2021-06-22 v2

Authors: Ilyas Khan

Abstract

In this paper, we prove that any mean curvature flow translator $\Sigma^2 \subset \mathbb{R}^3$ with finite total curvature and one end must be a plane. We also prove that if the translator $\Sigma$ has multiple ends, they are asymptotic to a plane $\Pi$ containing the direction of translation and can be written as graphs over $\Pi$ . Finally, we determine that the ends of $\Sigma$ are strongly asymptotic to $\Pi$ and obtain quantitative estimates for their asymptotic behavior.

Keywords

mean curvature flow translators finite total curvature asymptotic behavior differential geometry

Cite

@article{arxiv.2012.06926,
  title  = {The Structure of Translating Surfaces with Finite Total Curvature},
  author = {Ilyas Khan},
  journal= {arXiv preprint arXiv:2012.06926},
  year   = {2021}
}

Comments

26 Pages, significantly expanded: new results include asymptotic estimates and removal of conditions on area ratios. More detailed exposition, includes 2 new figures

Related papers

View all related →