Coplanar constant mean curvature surfaces

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

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Coplanar constant mean curvature surfaces

Karsten Grosse-Brauckmann·Robert B. Kusner·John M. Sullivan

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Abstract

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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BibTeX RIS

Karsten Grosse-Brauckmann, Robert B. Kusner, John M. Sullivan. 2007-12-05. Coplanar constant mean curvature surfaces. https://arxiv.org/abs/math/0509210

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