Rotators-Translators to Mean Curvature Flow in ${\mathbb{H}}^2\times \mathbb{R}$

Abstract

We establish the existence of one-parameter families of helicoidal surfaces of ${\mathbb{H}}^2\times \mathbb{R}$ which, under mean curvature flow, simultaneously rotate about a vertical axis and translate vertically.

10 pages, 4 figures. arXiv admin note: text overlap with arXiv:2307.14136