Communications in Analysis and Geometry

Volume 15 (2007)

Number 5

Coplanar constant mean curvature surfaces

Pages: 985 – 1023



Karsten Grosse-Brauckmann

Robert B. Kusner

John M. Sullivan


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.

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