, Volume 2, Issue 6, pp 517-554

Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We consider groups Γ generated by inversions in a pair of asymptotic complex hyperplanes in complex hyperbolic spaceH n . We show that there exists a Γ-invariant real hypersurfaceFH n such that the Dirichlet fundamental polyhedron for Γ centered at z0 has two sides (resp. infinitely many sides) if and only ifz 0F (resp.z 0F). The Dirichlet regions are determined explicitly in terms of coordinates on Γ-invariant horospheres and the geometry ofH n is developed in terms of these horospherical coordinates.

W. M. G.’s research partially supported by University of Maryland Institute of Advanced Computer Studies and National Science Foundation grant DMS-8902619. J. R. P.’s research partially supported by University of Maryland Institute for Physical Science and Technology.
Communicated by Karsten Grove