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Transactions of the American Mathematical Society

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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
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.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1984 American Mathematical Society