| Affiliation: | (1) Wesleyan University, Middletown, CT, USA;(2) University of Michigan, Ann Arbor, MI 48109, USA;(3) The University of Auckland, Auckland, New Zealand |
| Abstract: | We exhibit strong constraints on the geometry and topology of a uniformly quasiconformally homogeneous hyperbolic manifold. In particular, if n 3, a hyperbolic n-manifold is uniformly quasiconformally homogeneous if and only if it is a regular cover of a closed hyperbolic orbifold. Moreover, if n3, we show that there is a constant Kn>1 such that if M is a hyperbolic n-manifold, other than  which is K–quasiconformally homogeneous, then KKn.Mathematics Subject Classification (2000): 30C60Research supported in part by NSF grant 070335 and 0305704.Research supported in part by NSF grant 0203698.Research supported in part by the NZ Marsden Fund and the Royal Society (NZ).Research supported in part by NSF grant 0305704. |
