The topology and geometry of embedded surfaces of constant mean curvature (Q5916437)

It is shown that the annular ends of a surface of constant nonzero mean curvature are cylindrically bounded. This result is then used to show that a properly embedded surface of constant mean curvature in three- dimensional Euclidean space which is homeomorphic to a closed surface with one point removed must have zero mean curvature. Other geometric applications are made including a result which shows that the only foliation of 3-space by surfaces of constant mean curvature is by parallel planes.