Cylindrically bounded constant mean curvature surfaces in ${\mathbb{H}}^2\times \mathbb{R}$

Abstract

In this paper we prove that a properly embedded constant mean curvature surface in ${\mathbb{H}}^2\times \mathbb{R}$ which has finite topology and stays at a finite distance from a vertical geodesic line is invariant by rotation around a vertical geodesic line.

34 pages, 5 figures