Rotators-Translators to Mean Curvature Flow in \mathbb H²×\mathbb R

2024/02/07 by de Lima, Ronaldo F., Ramos, Álvaro K., Santos, João Paulo dos
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.04757

Abstract

We establish the existence of one-parameter families of helicoidal surfaces of \mathbb H²×\mathbb R which, under mean curvature flow, simultaneously rotate about a vertical axis and translate vertically.

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• Surfaces with prescribed mean curvature in ℍ²×ℝ
• Translators of the Gauss curvature flow
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• Rotational K^α-translators in Minkowski space
• Convex solutions to the mean curvature flow