Limit lamination theorem for H-disks

Abstract

In this paper we prove a theorem concerning 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 in [8]. 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 in [9] for minimal disks.