Limit lamination theorems for H-surfaces

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In this paper we prove some general results on constant mean curvature lamination limits of certain sequences of compact surfaces Mₙ embedded in R³ with constant mean curvature Hₙ 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.