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arXiv · 1803.02783

Translating solitons of the mean curvature flow in the space $\mathbb{H}^2\times\mathbb{R}$

Antonio Bueno
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Abstract

In this paper we study the theory of self translating solitons of the mean curvature flow of immersed surfaces in the product space $\mathbb{H}^2\times\mathbb{R}$. We relate this theory to the one of manifolds with density, and exploit this relation by regarding these translating solitons as minimal surfaces in a conformal metric space. Explicit examples of these surfaces are constructed, and we study the asymptotic behaviour of the existing rotationally symmetric examples. Finally, we prove some uniqueness and non-existence theorems.

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Antonio Bueno. 2018-03-07. Translating solitons of the mean curvature flow in the space $\mathbb{H}^2\times\mathbb{R}$. https://arxiv.org/abs/1803.02783

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