Coplanar constant mean curvature surfaces
微分几何
2007-12-05 v2
摘要
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.
引用
@article{arxiv.math/0509210,
title = {Coplanar constant mean curvature surfaces},
author = {Karsten Grosse-Brauckmann and Robert B. Kusner and John M. Sullivan},
journal= {arXiv preprint arXiv:math/0509210},
year = {2007}
}
备注
35 pages, 10 figures; minor revisions including one new figure; to appear in Comm. Anal. Geom