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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A theorem of Ahlfors for hyperbolic spaces


Author: Su Shing Chen
Journal: Trans. Amer. Math. Soc. 242 (1978), 401-406
MSC: Primary 22E40; Secondary 30F35
MathSciNet review: 496817
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Abstract: L. Ahlfors has proved that if the Dirichlet fundamental polyhedron of a Kleinian group G in the unit ball $ {B^3}$ has finitely many sides, then the normalized Lebesgue measure of $ L(G)$ is either zero or one. We generalize this theorem and a theorem of Beardon and Maskit to the n-dimensional case.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0496817-0
PII: S 0002-9947(1978)0496817-0
Keywords: Hyperbolic space, Kleinian group, limit set
Article copyright: © Copyright 1978 American Mathematical Society