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Quasiconformal groups with small dilatation. I. (English) Zbl 0984.30023
Quasiconformal Fuchsian groups with small dilatation are studied in this paper. A Jørgensen-type inequality in all dimensions is established for such a class of groups. It is shown that discreteness persists to the limit under algebraic convergence. Such groups are discrete if and only if every two generator subgroup is discrete.
Reviewer: Li Zhong (Beijing)

MSC:
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
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