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Quasiconformal homogeneity after Gehring and Palka. (English) Zbl 1307.30051
Summary: 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.

MSC:
30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
30F45 Conformal metrics (hyperbolic, Poincaré, distance functions)
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