Sarvas, Jukka Boundary of a homogeneous Jordan domain. (English) Zbl 0597.30024 Ann. Acad. Sci. Fenn., Ser. A I, Math. 10, 511-514 (1985). Let F(K) be the family of all K-quasiconformal mappings \(f: {\bar {\mathbb{C}}}\to {\bar {\mathbb{C}}}\), where \(1\leq K<\infty\). A set \(E\subset {\bar {\mathbb{C}}}\) is called homogeneous with respect to F(K) if for each \(z_ 1,z_ 2\in E\) there is an \(f\in F(K)\) with \(f(E)=E\) and \(f(z_ 1)=z_ 2\). The author proves the following characterization of quasidisks. Theorem. A Jordan domain D is a quasidisk if and only if D is homogeneous with respect to F(K) for some K, \(1\leq K<\infty.\) The proof of this interesting result is quite a straightforward (but non- trivial) application of a normal family argument. The theorem is connected with a result of T. Erkama [Mich. Math. J. 24, 157-159 (1977; Zbl 0363.30030)]. Reviewer: M.Vuorinen Cited in 3 Documents MSC: 30C62 Quasiconformal mappings in the complex plane Keywords:homogeneous Jordan domain; K-quasiconformal mappings; quasidisks; normal family Citations:Zbl 0363.30030 PDFBibTeX XMLCite \textit{J. Sarvas}, Ann. Acad. Sci. Fenn., Ser. A I, Math. 10, 511--514 (1985; Zbl 0597.30024) Full Text: DOI