极小曲面理论中一个完备引理在各类曲面中的应用
Applications of a completeness lemma in minimal surface theory to various classes of surfaces
摘要：
我们给出了几个应用程序的引理的完整性Osserman显示亚纯的Weierstrass数据完整的极小曲面有限的全曲率。定义了几类含有奇点的曲面的完备性和弱完备性。完备性引理是研究这些曲面类完备性的一种有用的方法。特别地，我们证明了de Sitter 3-空间中一个常中曲率为1（即CMC-1）的曲面是完备的当且仅当它是弱完备的，奇异集是紧的，并且所有端点共形等价于一个穿孔圆盘.
英文摘要：
We give several applications of a lemma on completeness used by Osserman to show the meromorphicity of Weierstrass data for complete minimal surfaces with finite total curvature. Completeness and weak completeness are defined for several classes of surfaces which admit singular points. The completeness lemma is a useful machinery for the study of completeness in these classes of surfaces. In particular, we show that a constant mean curvature one (i.e. CMC-1) surface in de Sitter 3-space is complete if and only if it is weakly complete, the singular set is compact and all the ends are conformally equivalent to a puntured disk.
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