Quasiconformal homogeneity of hyperbolic manifolds
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- Bonfert-Taylor, P., Canary, R., Martin, G. et al. Math. Ann. (2005) 331: 281. doi:10.1007/s00208-004-0582-6
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 n≥3, 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 K≥Kn.