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Discrete convergence groups. (English) Zbl 0623.30030
Complex analysis I, Proc. Spec. Year, College Park/Md. 1985-86, Lect. Notes Math. 1275, 158-167 (1987).
[For the entire collection see Zbl 0615.00005.]
The new class of discrete convergence groups is intended to capture the essential geometric properties of the old class of discrete groups of uniformly quasiconformal homeomorphisms. The authors cite results of Tukia,Martin, Freedman, and Skora which show that the new class is indeed larger than the old class. They then show how the new definitions may be used to establish results for the new class completely analogous to standard important results about the old class. For example, they show that elements may be naturally classified as elliptic, parabolic, or loxodromic under definitions which naturally extend the old definitions.
Reviewer: J.W.Cannon

MSC:
30C62 Quasiconformal mappings in the complex plane
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)