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The main aim of this paper is to give a complete solution to one of the openproblems, raised by Heinonen from 1989, concerning the subinvariance of Johndomains under quasiconformal mappings in $\IR^n$. As application, thequasisymmetry of quasiconformal mappings is discussed.

The quasiconformal subinvariance property of John domains in $\protect \IR^n$ and its application