A halfspace theorem for mean curvature surfaces in H2×R

We prove a vertical halfspace theorem for surfaces with constant mean curvature , properly immersed in the product space H2×R, where H2 is the hyperbolic plane and R is the set of real numbers. The proof is a geometric application of the classical maximum principle for second order elliptic PDE, using the family of noncompact rotational surfaces in H2×R.