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Discrete Quasiconformal Groups I
Author(s) -
Gehring F. W.,
Martin G. J.
Publication year - 1987
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1093/plms/s3-55_2.331
Subject(s) - haven , citation , library science , foundation (evidence) , sociology , mathematics , history , computer science , combinatorics , archaeology
In this short paper, we introduce a geometry of discrete quasiconformal groups. This subject has been studied by several mathematicians, name them few, P. Tukia, G. Martin, F. Gehring, D. Sullivan. This is an application of the quasiconformal mappings. For n ≥ 2, we let R denote euclidean n−space, Rn its one point compactification R ∪ {∞} and e1, · · · , en the standard orthonormal basis for R. A Möbius transformation acting on Rn is a finite composition of reflections in spheres and hyperplanes ; we let Möb(n) denote the group of all such transformations. Denote M(n) a group of orientation preserving Möbius transformations which is a subset of Möb(n). Stereographic projection p is the mapping from Rn into the unit sphere S in R given by