Arcwise connected domains, quasiconformal mappings, and quasidisks
Summary: We prove that a homeomorphism \(f : R^2 \rightarrow R^2\) is a quasiconformal mapping if and only if \(f(D)\) is an arcwise connected domain for any arcwise connected domain \(D \subseteq R^2\), and \(D\) is a quasidisk if and only if both \(D\) and its exterior \(D^* = R^2 \smallsetminus \overline{D}\) are arcwise connected domains.
scientific article; zbMATH DE number 7022359
scientific article