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arXiv · 2402.05533

A new family of translating solitons in hyperbolic space

Antonio Bueno·Rafael López
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Abstract

If $\xi$ is a Killing vector field of the hyperbolic space $\h^3$ whose flow are parabolic isometries, a surface $\Sigma\subset\h^3$ is a $\xi$-translator if its mean curvature $H$ satisfies $H=\langle N,\xi\rangle$, where $N$ is the unit normal of $\Sigma$. We classify all $\xi$-translators invariant by a one-parameter group of rotations of $\h^3$, exhibiting the existence of a new family of grim reapers. We use these grim reapers to prove the non-existence of closed $\xi$-translators.

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Antonio Bueno, Rafael López. 2024-02-08. A new family of translating solitons in hyperbolic space. https://arxiv.org/abs/2402.05533

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