Cylindrically bounded constant mean curvature surfaces in   $\mathbb{H}^2\times\mathbb{R}$
  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. 
Laurent Mazet
math.DG