Some results on translating solitons of the mean curvature flow

Jesús Pérez-García

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arXiv · 1601.07287

Some results on translating solitons of the mean curvature flow

Jesús Pérez-García

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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.

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Jesús Pérez-García. 2016-01-27. Some results on translating solitons of the mean curvature flow. https://arxiv.org/abs/1601.07287

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