DIRICHLET POLYHEDRA FOR CYCLIC GROUPS IN COMPLEX HYPERBOLIC SPACE

We prove that the Dirichlet fundamental polyhedron for a cyclic group generated by a unipotent or hyperbolic element-gamma acting on complex hyperbolic n-space centered at an arbitrary point omega is bounded by the two hypersurfaces equidistant from the pairs omega, gamma-omega and omega, gamma-1 omega respectively. The proof relies on a convexity property of the distance to an isometric flow containing gamma .