We study translators of the mean curvature flow in the product space ²×, that is, self-similar solutions whose shape is invariant by translations of ²×. In ²× there are three types of translations: vertical translations due to the factor and parabolic and hyperbolic translations from ². A grim reaper in ²× is a translators invariant by a one-parameter group of translations. The variety of translators and translations in ²× makes that the family of grim reapers particularly rich. In this paper we give a full classification of the grim reapers of ²× with a description of their geometric properties. In some cases, we obtain explicit parametrizations of the surfaces.
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Bueno et al. (2024) studied this question.
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