A halfspace theorem for mean curvature H=12 surfaces in H2×R

Abstract

We prove a vertical halfspace theorem for surfaces with constant mean curvature H = 1 2 , properly immersed in the product space H 2 × R, where H 2 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 H = 1 2 surfaces in H 2 × R.