Bonfert-Taylor, Petra; Canary, Richard D.; Martin, Gaven; Taylor, Edward C.; Wolf, Michael Ambient quasiconformal homogeneity of planar domains. (English) Zbl 1198.30017 Ann. Acad. Sci. Fenn., Math. 35, No. 1, 275-283 (2010). An open set \(\Omega \subset {\overline{\mathbb C}}\) is ambiently \(K\)-quasiconformally homogeneous if, for all \(x, y \in \Omega\), there exists a \(K\)-quasiconformal homeomorphism \(f : {\overline{\mathbb C}} \to {\overline{\mathbb C}}\) such that \(f(x) = y\) and \(f(\Omega) =\Omega\).The authors prove that the ambient quasiconformal homogeneity constant of a hyperbolic planar domain, which is not simply connected, is uniformly bounded away from \(1\). Reviewer: Matti Vuorinen (Turku) Cited in 3 Documents MSC: 30C62 Quasiconformal mappings in the complex plane 30F45 Conformal metrics (hyperbolic, Poincaré, distance functions) Keywords:quasiconformal homogeneity PDFBibTeX XMLCite \textit{P. Bonfert-Taylor} et al., Ann. Acad. Sci. Fenn., Math. 35, No. 1, 275--283 (2010; Zbl 1198.30017) Full Text: DOI