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

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.