Publication date:
7 September 2017
Source:Advances in Mathematics, Volume 317
Author(s): Baris Coskunuzer
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 $H_0$-convex domain is embedded for any $H\in [0,H_0)$. In particular, for the unit ball B in ${\mathbb{R}}^3$, this implies that for any $H\in [0,1]$, any Jordan curve in $\partial \mathbf{B}$ bounds an embedded H-disk in B.