On the classification of Kleinian groups: I—Koebe groups
On the classification of Kleinian groups: I—Koebe groups
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关于克莱因群的分类：I—Koebe群
DOI：
10.1007/bf02392021
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发表时间：
1975
期刊：
影响因子：
3.7
通讯作者：
B. Maskit
中科院分区：
文献类型：
--
作者：
B. Maskit
本文给出了一类Klein群，称为Koebe群，证明了闭Riemann曲面的每一个非形式化都可以由唯一的Koebe群实现.第一个例子，这些团体是由于克莱因[6]谁建造他们使用他的组合定理。Koebe [7，8]证明了一个一般的非形式化定理的克莱因]一群构造在这种方式。我们的存在性定理是以广义组合定理[11，12]为基础的，并使用了Bers的拟共形映射变参数技巧[3]。唯一性定理是Koebe原证明[7]的推广，但有较弱的假设。定理的详细陈述和证明的大纲出现在第2节。这些定理都是用克莱因群来表述的;用黎曼曲面的非形式化来表述的等价公式出现在[13]中，我们的主要结果是在[13]中首次宣布的。
In this paper we exhibit a class of Klein]an groups called Koebe groups, and prove tha t every un]formization of a closed Riemann surface can be realized by a unique Koebe group. The first examples of these groups were due to Klein [6] who constructed them using his combination theorem. Koebe [7, 8] proved a general un]formization theorem for Klein]an groups constructed in this fashion. Our existence theorem is based on the generalized combination theorems [11, 12], and uses Bers' technique of variation of parameters using quasiconformal mappings [3]. The uniqueness theorem is a generalization of Koebe 's original proof [7], but with weaker hypotheses. Detailed statements of theorems, and outlines of proofs appear in section 2. The theorems are all formulated in terms of Klein]an groups; equivalent formulations in terms of un]formizations of Riemann surfaces appear in [13], where our main result was first announced.