John disks and \(K\)-quasiconformal harmonic mappings (Q2012963)

Let \(f : \mathbb{D} \to G\) be a conformal map onto a bounded domain \(G\) of the complex plane. \textit{Ch. Pommerenke} [J. Lond. Math. Soc., II. Ser. 26, 77--88 (1982; Zbl 0464.30012)] has proved that \(G\) is a hyperbolic John disk iff the derivative of \(f\) satisfies a certain growth condition. The authors extend this result to the case of quasiconformal maps.