Some results on translating solitons of the mean curvature flow

2016/01/27 by Pérez-García, Jesús
#53A10 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.07287

Abstract

In this article we prove two non-existence results for translating solitons of the mean curvature flow (translators for short) in ℝ^m+1. We also obtain an upper bound to the maximum height that a compact embedded translator in ℝ³ 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.

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