Remote Access Transactions of the American Mathematical Society
Green Open Access

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
MathSciNet review: 728717
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] L. V. Ahlfors, Hyperbolic motions, Nagoya Math. J. 29 (1967), 163-166. MR 0233976 (38:2297)
  • [2] A. F. Beardon and P. J. Nicholls, Ford and Dirichlet regions for Fuchsian groups, Canad. J. Math. 34 (1982), 806-815. MR 672677 (84h:30072)
  • [3] P. J. Nicholls, Garnett points for Fuchsian Groups, Bull. London Math. Soc. 12 (1980), 216-218. MR 572105 (82b:30056)
  • [4] Ch. Pommerenke, On the Green's function of Fuchsian groups, Ann. Acad. Sci. Fenn. A I Math. 2 (1976), 409-427. MR 0466534 (57:6412)
  • [5] V. G. Sprindzuk, Metric theory of Diophantine approximation, Wiley, New York, 1979. MR 548467 (80k:10048)
  • [6] D. Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, in Riemann Surfaces and Related Topics, Ann. of Math. Studies, no. 97, Princeton Univ. Press, Princeton, N. J., 1980, pp. 465-496. MR 624833 (83f:58052)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30F35, 20H10, 58F11

Retrieve articles in all journals with MSC: 30F35, 20H10, 58F11

Additional Information

Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society