8 February 2024
There are 3 types of translations in this space: vertical, parabolic, hyperbolic
A 'grim reaper' is a translator invariant under 1-parameter group of translations
Vertical, parabolic, hyperbolic v-grim reapers are studied
Vertical and parabolic p-grim reapers and c+-, c--grim reapers also classified
Some grim reapers given explicit parametrizations, geometric properties described
Classification of self-similar translators in hyperbolic plane times Euclidean line
This paper classifies 'grim reaper' translators in the product space of the hyperbolic plane and a Euclidean line. These are surfaces that evolve self-similarly under mean curvature flow, staying invariant under certain translation groups. The authors give a full classification of 9 types of these translators, studying their geometric properties and in some cases finding explicit parametrizations.
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