Published on:

8 February 2024

Primary Category:

Differential Geometry

Paper Authors:

Antonio Bueno,

Rafael López

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There are 3 types of translations in this space: vertical, parabolic, hyperbolic

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A 'grim reaper' is a translator invariant under 1-parameter group of translations

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Vertical, parabolic, hyperbolic v-grim reapers are studied

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Vertical and parabolic p-grim reapers and c+-, c--grim reapers also classified

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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.

Simplified classification of hyperbolic space horo-shrinkers

Helicoidal surfaces flowing by mean curvature in H^2 x R

Solitons of surfaces evolving by mean curvature in the sphere cross the line

Classifying special generalized quadrangles and related structures

Poincare inequality for translators and self-expanders

Classification of special triharmonic curves in 3D Sol space

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