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Coplanar constant mean curvature surfaces. (English) Zbl 1145.53002

Summary: We consider constant mean curvature surfaces with finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors. Here, we extend the arguments to the case of an arbitrary number of ends, under the assumption that the asymptotic axes of the ends lie in a common plane: we construct and classify the entire family of these genus-zero, coplanar constant mean curvature surfaces.

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
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