Covolume estimates for discrete groups of hyperbolic isometries having parabolic elements (Q1330154)

We address the problem of estimating the covolume of a discrete group of orientation-preserving isometries of hyperbolic space in any dimension. We provide a general method for obtaining a lower bound for the covolume in the case that the group has parabolic elements. For a torsion-free discrete group of orientation-preserving isometries of hyperbolic 4-space having parabolic elements, we give an explicit lower bound.