On the topology of constant mean curvature surfaces in H2 X R with boundary in a plane

Abstract

A gap in the proof prevents us to show that surfaces with constant mean curvature closed to 1/2 in H2 X R and having boundary with curvature greater than one, contained in a horizontal section P of H2 X R are topological disks, provided they are contained in one of the two halfspaces determined by P. This is the analogue in H2 X R of a result in R3 by A. Ros and H. Rosenberg [13, Theorem 2].