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