Domain constants and quasiconformal maps (Q892225)

The hyperbolic metric is not quasi-invariant under quasiconformal mappings but is quasi-invariant under unidirectional stretchings of convex region [\textit{R. Bañuelos} and \textit{T. Carroll}, Q. J. Math. 61, No. 3, 265--273 (2010; Zbl 1213.30004)] and under harmonic quasiconformal mappings [\textit{X. Chen} and \textit{A. Fang}, J. Math. Anal. Appl. 369, No. 1, 22--28 (2010; Zbl 1194.30027)]. Several domain constants associated with the hyperbolic metric are quasi-invariant under quasiconformal mappings. The authors study the behaviour of such domain constants.