Mathematische Annalen

, Volume 331, Issue 2, pp 281–295

Quasiconformal homogeneity of hyperbolic manifolds

  • Petra Bonfert-Taylor
  • Richard D. Canary
  • Gaven Martin
  • Edward Taylor
Article

DOI: 10.1007/s00208-004-0582-6

Cite this article as:
Bonfert-Taylor, P., Canary, R., Martin, G. et al. Math. Ann. (2005) 331: 281. doi:10.1007/s00208-004-0582-6

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 n≥3, we show that there is a constant Kn>1 such that if M is a hyperbolic n-manifold, other than https://static-content.springer.com/image/art%3A10.1007%2Fs00208-004-0582-6/MediaObjects/s00208-004-0582-6flb1.gif which is K–quasiconformally homogeneous, then KKn.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Petra Bonfert-Taylor
    • 1
  • Richard D. Canary
    • 2
  • Gaven Martin
    • 3
  • Edward Taylor
    • 1
  1. 1.Wesleyan UniversityMiddletownUSA
  2. 2.University of MichiganAnn ArborUSA
  3. 3.The University of AucklandAucklandNew Zealand