Coplanar constant mean curvature surfaces

Grosse-Brauckmann, Karsten; Kusner, Robert B.; Sullivan, John M.

Coplanar constant mean curvature surfaces

Authors

Grosse-Brauckmann, Karsten

Kusner, Robert B.

Sullivan, John M.

Description

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