On cusp regions associated to screw-parabolic maps

Erlandsson and Zakeri gave a very precise description of the Margulis region associated to cusps of hyperbolic 4-manifolds associated to screw-parabolic maps. We give some bounds on the asymptotic shape of these regions that improve on the results of Erlandsson and Zakeri. We also describe similar regions coming from work of Waterman. Finally, we generalise these results to complex hyperbolic 2-space.