On the analytic theory of quasi-finitely generated Kleinian groups. III, IV. (Chinese. English summary) Zbl 0789.30034

Wang, Jian; Cai, Huijing

Nat. Sci. J. Xiangtan Univ. 14, No. 2, 40-47 (1992).

A Kleinian group \(\Gamma\) is said to be quasi-finitely generated if it can be represented by \(\Gamma=\langle \gamma_ 1,\dots,\gamma_ n,\;\Gamma(B) \rangle\), where \(\Gamma(B)\) is the maximal annihilated subgroup. In this paper, the finiteness theorem of Ahlfors is generalized to the quasi-finitely generated Kleinian groups. Many other classical results of finitely generated Kleinian groups are also generalized, such as the area theorem, area inequalities and the estimations of cusps.

Reviewer: Li Zhong (Beijing)

MSC:

30F40

Kleinian groups (aspects of compact Riemann surfaces and uniformization)