Mathematische Annalen

, Volume 331, Issue 2, pp 281-295

First online:

Quasiconformal homogeneity of hyperbolic manifolds

  • Petra Bonfert-TaylorAffiliated withWesleyan University
  • , Richard D. CanaryAffiliated withUniversity of Michigan Email author 
  • , Gaven MartinAffiliated withThe University of Auckland
  • , Edward TaylorAffiliated withWesleyan University

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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 K n >1 such that if M is a hyperbolic n-manifold, other than which is K–quasiconformally homogeneous, then KK n .