The quasiconformal subinvariance property of John domains in \({\mathbb {R}}^n\) and its applications (Q500269)

Let \(f: D \to D'\) be a quasiconformal homeomorphism between domains \(D, D' \subset {\mathbb R}^n\,.\) The authors study the so-called subinvariance problem for John domains, previously studied by J. Heinonen and J. Väisälä, and give a complete solution of the problem. The main result says that if \(D\) and \(D'\) are bounded and \(D'\) is a John domain, then for every John domain \(D_1 \subset D\), the image \(f(D_1)\) is a John domain, too.