The existence of surfaces of constant mean curvature with free boundaries
The existence of surfaces of constant mean curvature with free boundaries
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DOI：
10.1007/bf02392272
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发表时间：
1988-07
期刊：
影响因子：
3.7
通讯作者：
M. Struwe
中科院分区：
文献类型：
--
作者：
M. Struwe
设S是R3中的一个曲面，S通过C4类光滑双同态W：R3--> R3与标准球面S2双同态，设HER.本文给出了一个不稳定的常平均曲率圆盘型曲面H存在的充分条件，该曲面的边界在S上，且与S沿其边界沿着正交.在等温坐标中，这样的表面可以由单位圆盘的映射XE C2（B; R3）N cl（l ~; R3）参数化
Suppose S is a surface in R 3 diffeomorphic to the standard sphere S 2 by a smooth diffeomorphism W: R3--> R 3 of class C 4, and let HER. In this paper we give a sufficient condition for the existence of an unstable disc-type surface of constant mean curvature H with boundary on S and intersecting S orthogonally along its boundary. In isothermal coordinates such a surface may be parametrized by a map XE C2 (B; R3) N cl (/~; R 3) of the unit disc