Limit lamination theorem for H-disks

Abstract

We describe the lamination limits of sequences of compact disks M_n embedded in {mathbb {R}}^3 with constant mean curvature H_n, when the boundaries of these disks tend to infinity. This theorem generalizes to the non-zero constant mean curvature case Theorem 0.1 by Colding and Minicozzi (Ann Math 160:573–615, 2004) for minimal disks. We apply this theorem to prove the existence of a chord arc result for compact disks embedded in {mathbb {R}}^3 with constant mean curvature; this chord arc result generalizes Theorem 0.5 by Colding and Minicozzi (Ann Math 167:211–243, 2008) for minimal disks.