Complete properly immersed translators in H2 × R have asymptotic boundary components that are vertical lines, vertical rays, or complete geodesics.
Translating solitons of the mean curvature flow in the space H2 × R
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On the geometry of the asymptotic boundary of translators in $\mathbb H^2\times \mathbb R$
Complete properly immersed translators in H2 × R have asymptotic boundary components that are vertical lines, vertical rays, or complete geodesics.