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arXiv · 2405.15957

Translators of the mean curvature flow in the special linear group $SL(2,\mathbb{R})$

Rafael López·Marian Ioan Munteanu
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Abstract

Translators in the special linear group $SL(2,\mathbb{R})$ are surfaces whose mean curvature $H$ and unit normal vector $N$ satisfy $H=\langle N,X\rangle$, where $X$ is a fixed Killing vector field. In this paper we study and classify those translators that are invariant by a one-parameter group of isometries. By the Iwasawa decomposition, there are three types of such groups. The dimension of the Killing vector fields is $4$ and an exhaustive discussion is done for each one of the Killing vector fields and each of the invariant surfaces. In some cases, explicit parametrizations of translators are obtained.

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Rafael López, Marian Ioan Munteanu. 2024-05-24. Translators of the mean curvature flow in the special linear group $SL(2,\mathbb{R})$. https://arxiv.org/abs/2405.15957

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