Resumen de Slab theorem and halfspace theorem for constant mean curvature surfaces in H2 R

Laurent Hauswirth, Ana Menezes, Magdalena Rodríguez

• We prove that a properly embedded annular end of a surface in H2 R with constant mean curvature 0 < H 1=2 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H 1=2 contained in H2 Œ0; C1/ and with finite topology is necessarily a graph over a simply connected domain of H2 . For the case H D 1=2, the graph is entire.