Coplanar constant mean curvature surfaces
Coplanar constant mean curvature surfaces
复制标题
共面常平均曲率曲面
DOI：
10.4310/cag.2007.v15.n5.a4
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发表时间：
2005
影响因子：
0.7
通讯作者：
J. Sullivan
中科院分区：
文献类型：
--
作者：
Karsten Große;R. Kusner;J. Sullivan
我们考虑在Alexandrov意义下适当嵌入到三维空间中的具有有限拓扑的常平均曲率曲面。作者(GKS2，GKS1)构造了这种具有三端亏格零的曲面，并对其进行了完全分类。在此，我们将其结果推广到任意端点数的情形，在端点渐近轴位于公共平面的假设下：我们构造并分类了这类亏格为零的共面常平均曲率曲面族。
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 com- pletely classified by the authors (GKS2, GKS1). Here we extend the arguments to the case of an arbitrary number of ends, under the as- sumption 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.