A new family of translating solitons in hyperbolic space

Abstract

If $\hat{I}¾$ is a Killing vector field of the hyperbolic space $\h^3$ whose flow are parabolic isometries, a surface $Σ\subset\h^3$ is a $\hat{I}¾$-translator if its mean curvature $H$ satisfies $H=⟨N,\hat{I}¾⟩$, where $N$ is the unit normal of $\hat{I}\pounds$. We classify all $\hat{I}¾$-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 $\hat{I}¾$-translators.

11 pages, 2 figures