具有特殊类型端口的极小曲面的构造

Construction of Minimal Surfaces with Special Type Ends

中文关键词:  极小曲面  全曲率  端口  环绕指标.

英文关键词:minimal surface  total curvature  end  winding order.

中文摘要:

      我们证明了在$R^3$中存在这样一族具有全曲率$-4n\pi$的完备的定向极小曲面,它们具有亏格$0$和两个环绕指标为$n$的端口,其中$n=1, 2, 3,\ldots$, 并讨论了它们在某些特定参数下的对称性.

英文摘要:

      We proved that there exists a family of complete oriented minimal surfaces in ${\mathbb{R}}^3$ with finite total curvature $-4n\pi$, each of which has $0$ genus and two ends, and both of the ends have winding order $n$, where $n\in\mathbb{N}$, and discussed the symmetric property for special parameters.