Embeddedness of the solutions to the H-Plateau problem

Abstract

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 H0-convex domain is embedded for any H∈[0,H0). In particular, for the unit ball B in R3, this implies that for any H∈[0,1], any Jordan curve in ∂B bounds an embedded H-disk in B.