Abstract
We study translators of the mean curvature flow in the product space H2×R. In H2×R there are three types of translations: vertical translations due to the factor R and parabolic and hyperbolic translations from H2. A grim reaper in H2×R is a translator invariant by a one-parameter group of translations. The variety of translators and translations in H2×R makes the family of grim reapers particularly rich. In this paper we give a full classification of the grim reapers of H2×R with a description of their geometric properties. In some cases, we obtain explicit parametrizations of the surfaces.
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