Some results on translating solitons of the mean curvature flow

Abstract

In this article we prove two non-existence results for translating solitons of the mean curvature flow (translators for short) in ${\mathbb{R}}^{m+1}$. We also obtain an upper bound to the maximum height that a compact embedded translator in ${\mathbb{R}}^3$ can achieve. On the other hand, we study graphical perturbations of translators, showing that asymptotic graphical perturbations of a graph translator of revolution remain a hypersurface of revolution. Finally, we prove that compact translators that lie between two parallel planes inherit the symmetries of their boundaries curves.

20 pages, 3 figures

References in corpus (1)

• Non-existence for self-translating solitons

Cited by in corpus (1)

• Bi-Halfspace and Convex Hull Theorems for Translating Solitons