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 , 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