Hjelle, Geir Arne A simply connected, homogeneous domain that is not a quasidisk. (English) Zbl 1071.30018 Ann. Acad. Sci. Fenn., Math. 30, No. 1, 135-142 (2005). Let \(K \geq 1\) and let \({\mathcal F}(K)\) be the class of all \(K\)-quasiconformal maps of \({\overline {\mathbb C}}\, .\) A set \(S \subset {\overline {\mathbb C}}\) is said to be homogeneous with respect to \({\mathcal F}(K)\) if for each pair \(z_1, z_2 \in S\) there exists a mapping \( f \in {\mathcal F}(K)\) with \(f(S) = S\) and \(f(z_1)=z_2 \,.\) The author constructs a simply connected domain \(D\,,\) homogeneous with respect to \({\mathcal F}(K)\,\) for some \(K>1\,,\) that is not a quasidisk. Reviewer: Matti Vuorinen (Turku) Cited in 2 Documents MSC: 30C62 Quasiconformal mappings in the complex plane Keywords:quasiconformal maps PDFBibTeX XMLCite \textit{G. A. Hjelle}, Ann. Acad. Sci. Fenn., Math. 30, No. 1, 135--142 (2005; Zbl 1071.30018) Full Text: EuDML