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, catenoidtype surfaces, and exhibit a classification result when the prescribed function is linear.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 arXiv:
 arXiv:2012.03795
 Bibcode:
 2020arXiv201203795B
 Keywords:

 Mathematics  Differential Geometry;
 53A10;
 53C42;
 34C05;
 34C40