Surfaces with prescribed mean curvature in $\mathbb{H}^2\times\mathbb{R}$

Antonio Bueno; Irene Ortiz

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arXiv · 2012.03795

Surfaces with prescribed mean curvature in $\mathbb{H}^2\times\mathbb{R}$

Antonio Bueno·Irene Ortiz

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Abstract

In this paper we study rotational surfaces in the space $\mathbb{H}^2\times\mathbb{R}$ whose mean curvature is given as a prescribed function of their angle function. These surfaces generalize, among others, the ones of constant mean curvature and the translating solitons of the mean curvature flow. Using a phase plane analysis we construct entire rotational graphs, catenoid-type surfaces, and exhibit a classification result when the prescribed function is linear.

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Antonio Bueno, Irene Ortiz. 2020-12-07. Surfaces with prescribed mean curvature in $\mathbb{H}^2\times\mathbb{R}$. https://arxiv.org/abs/2012.03795

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