On pseudo-metrics on the space of generalized quasisymmetric automorphisms of a Jordan curve (Q2769242)

The paper deals with quasiconformal mappings in the plane. Let \(\Omega\) be a Jordan domain then it is well-known that a quasiconformal self-mapping of \(\Omega\) has a homeomorphic extension of the closure \(\overline \Omega= \Omega\cup \Gamma\) onto itself. If we denote by \(H^+(\Gamma)\) the set of all sense-preserving homeomorphic mappings of \(\Gamma\), the main topic of the paper is to construct functionals \(\rho:H^+ (\Gamma)\times H^+(\Gamma) \to[0, \infty]\) which satisfy some properties, for example to be a pseudometric.