Embeddedness of the solutions to the H-Plateau problem

We generalize Meeks and Yau's embeddedness result on the solutions of the Plateau problem to constant mean curvature disks. We show that any minimizing H-disk in an Ho-convex domain is embedded for any H is an element of [0, H-0). In particular, for the unit ball B in R-3, this implies that for any H is an element of [0,1], any Jordan curve in partial derivative B bounds an embedded H-disk in B. (C) 2017 Elsevier Inc. All rights reserved.