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arXiv · 1904.12015

A family of MCF solutions for the Heisenberg Group

Benedito Leandro·Adriana Araujo Cintra·Hiuri Fellipe dos Santos Reis
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Abstract

The aim of this paper is to investigate the mean curvature flow soliton solutions on the Heisenberg group $\mathcal{H}$ when the initial data is a ruled surface by straight lines. We give a family of those solutions which are generated by $\mathfrak{Iso}_{0}(\mathcal{H})$ (the isometries of $\mathcal{H}$ for which the origin is a fix point). We conclude that the function which describe the motion of these surfaces under MCF, is always a linear affine function. As an application we proof that the Grim Reaper solution evolves from a ruled surface in $\mathcal{H}$. We also provide other examples.

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Benedito Leandro, Adriana Araujo Cintra, Hiuri Fellipe dos Santos Reis. 2019-04-26. A family of MCF solutions for the Heisenberg Group. https://doi.org/10.1016/j.difgeo.2020.101633

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