# Quasiconformal Homogeneity after Gehring and Palka

Quasiconformal Homogeneity after Gehring and Palka In a very influential paper Gehring and Palka introduced the notions of quasiconformally homogeneous and uniformly quasiconformally homogeneous subsets of $$\overline{\mathbb {R}}^n$$ R ¯ n . Their definition was later extended to hyperbolic manifolds. In this paper we survey the theory of quasiconformally homogeneous subsets of $$\overline{\mathbb {R}}^n$$ R ¯ n and uniformly quasiconformally homogeneous hyperbolic manifolds. We furthermore include a discussion of open problems in the theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

# Quasiconformal Homogeneity after Gehring and Palka

, Volume 14 (3) – Mar 29, 2014
14 pages

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Publisher
Springer Journals
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-014-0057-z
Publisher site
See Article on Publisher Site

### Abstract

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

### Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 29, 2014

### References

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