Coplanar constant mean curvature surfaces

Details Coplanar constant mean curvature surfaces Coplanar constant mean curvature surfaces

2005-09-09

arxiv.org/abs/math/0509210v2

Mathematics

Differential Geometry

35 pages, 10 figures; minor revisions including one new figure; to appear in Comm. Anal. Geom

Scientific paper

We consider constant mean curvature surfaces of 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 in arXiv:math.DG/0102183. 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.

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