Ford and Dirichlet regions for discrete groups of hyperbolic motions

Nicholls, P. J.

doi:10.1090/S0002-9947-1984-0728717-5

Ford and Dirichlet regions for discrete groups of hyperbolic motions
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by P. J. Nicholls PDF

Trans. Amer. Math. Soc. 282 (1984), 355-365 Request permission

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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