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Classification of self-similar translators in hyperbolic plane times Euclidean line

Published on:

8 February 2024

Primary Category:

Differential Geometry

Paper Authors:

Antonio Bueno,

Rafael López

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Key Details

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

AI generated summary

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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