Limit lamination theorems for H-surfaces

In this paper we prove some general results on constant mean curvature lamination limits of certain sequences of compact surfaces $M_n$ embedded in ${\mathbb{R}}^3$ with constant mean curvature $H_n$ and fixed finite genus, when the boundaries of these surfaces tend to infinity. Two of these theorems generalize to the non-zero constant mean curvature case, similar structure theorems by Colding and Minicozzi in~[6,8] for limits of sequences of minimal surfaces of fixed finite genus.