Limit lamination theorem for H-disks

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