A Schoen theorem for minimal surfaces in H2×R

In this paper we prove that a complete minimal surface immersed in H2×R, with finite total curvature and two ends, each one asymptotic to a vertical geodesic plane, must be a horizontal catenoid. Moreover, we give a geometric description of minimal ends of finite total curvature in H2×R. We also prove that a minimal complete end E with finite total curvature is properly immersed and that the Gaussian curvature of E is locally bounded in terms of the geodesic distance to its boundary.