The Journal of Geometric Analysis

, Volume 2, Issue 6, pp 517–554

Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space

  • William M. Goldman
  • John R. Parker

DOI: 10.1007/BF02921576

Cite this article as:
Goldman, W.M. & Parker, J.R. J Geom Anal (1992) 2: 517. doi:10.1007/BF02921576


We consider groups Γ generated by inversions in a pair of asymptotic complex hyperplanes in complex hyperbolic spaceHn. We show that there exists a Γ-invariant real hypersurfaceFHn such that the Dirichlet fundamental polyhedron for Γ centered at z0 has two sides (resp. infinitely many sides) if and only ifz0F (resp.z0F). The Dirichlet regions are determined explicitly in terms of coordinates on Γ-invariant horospheres and the geometry ofHn is developed in terms of these horospherical coordinates.

Copyright information

© CRC Press, Inc 1992

Authors and Affiliations

  • William M. Goldman
    • 1
  • John R. Parker
    • 2
  1. 1.University of MarylandDepartment of MathematicsCollege, ParkUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK