Abstract
In this paper, we describe a large class of groups of isometries of thed-dimensional hyperbolic space. These groups may be non-geometrically finite but their Patterson-Sullivan measure is always finite.
Similar content being viewed by others
References
A. Ancona,Exemples de surfaces hyperboliques de type divergent, de mesure de Sullivan associées finies mais non géométriquement finies, Preprint.
L. Bers,On boundaries of Teichmüller spaces and on Kleinian groups, Annals of Mathematics91 (1970), 570–600.
C. J. Bishop and P. W. Jones,Hausdorff dimension and kleinian groups, Acta Mathematica179 (1997), 1–39.
B. Bowditch,Geometrical finiteness with variable negative curvature, Duke Mathematical Journal77 (1995), 229–274.
F. Dal’bo, J. P. Otal and M. Peigné,Séries de Poincaré des groupes géométriquement finis, Israel Journal of Mathematics118 (2000), 109–124.
H. Furusawa,Poincaré series of combination groups, The Tôhoku Mathematical Journal43 (1991), 1–7.
E. Hamilton,Geometrical finiteness for hyperbolic orbifolds, Topology37 (1998), 635–657.
B. Maskit,Kleinian Groups, A Series of Comprehensive Studies in Mathematics, Springer-Verlag, Berlin, 1987.
S. J. Patterson,The limit set of a Fuchsian group, Acta Mathematica136 (1976), 241–273.
S. J. Patterson,The exponent of convergence of Poincaré series, Monatshefte für Mathematik82 (1976), 297–315.
Th. Roblin,Sur la théorie ergodique des groupes discrets en géométrie hyperbolique, Thèse de doctorat de l’Université d’Orsay, 1999.
D. Sullivan,The density at infinity of a discrete group of hyperbolic motions, Publications Mathématiques de l’Institut des Hautes Études Scientifiques50 (1979), 171–202.
D. Sullivan,Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Mathematica153 (1984), 259–277.
D. Sullivan,Discrete conformal groups and measurable dynamics, Bulletin of the American Mathematical Society6 (1984), 57–73.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Peigné, M. On the Patterson-Sullivan measure of some discrete group of isometries. Isr. J. Math. 133, 77–88 (2003). https://doi.org/10.1007/BF02773062
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02773062