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Computational Methods and Function Theory

, Volume 14, Issue 2–3, pp 417–430 | Cite as

Quasiconformal Homogeneity after Gehring and Palka

  • Petra Bonfert-TaylorEmail author
  • Richard CanaryEmail author
  • Edward C. Taylor
Article

Abstract

In a very influential paper Gehring and Palka introduced the notions of quasiconformally homogeneous and uniformly quasiconformally homogeneous subsets of \(\overline{\mathbb {R}}^n\). Their definition was later extended to hyperbolic manifolds. In this paper we survey the theory of quasiconformally homogeneous subsets of \(\overline{\mathbb {R}}^n\) and uniformly quasiconformally homogeneous hyperbolic manifolds. We furthermore include a discussion of open problems in the theory.

Keywords

Quasiconformal homogeneity Hyperbolic surfaces 

Mathematics Subject Classification (2000)

Primary 30C (or more specifically 30C62) Secondary 30F (or more specifically 30F45) 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Wesleyan UniversityMiddletownUSA
  2. 2.University of MichiganAnn ArborUSA
  3. 3.National Science FoundationArlingtonUSA

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