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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Ford and Dirichlet regions for discrete groups of hyperbolic motions


Author: P. J. Nicholls
Journal: Trans. Amer. Math. Soc. 282 (1984), 355-365
MSC: Primary 30F35; Secondary 20H10, 58F11
DOI: https://doi.org/10.1090/S0002-9947-1984-0728717-5
MathSciNet review: 728717
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Abstract: It is shown that for a discrete group of hyperbolic motions of the unit ball of $ {\mathbf{R}^n}$, there is a single construction of fundamental regions which gives the Ford and Dirichlet regions as special cases and which also yields fundamental regions based at limit points. It is shown how the region varies continuously with the construction.

The construction is connected with a class of limit points called Garnett points. The size of the set of such points is investigated.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0728717-5
Article copyright: © Copyright 1984 American Mathematical Society