The quasiconformal subinvariance property of John domains in $\protect   \IR^n$ and its application
  The main aim of this paper is to give a complete solution to one of the open problems, raised by Heinonen from 1989, concerning the subinvariance of John domains under quasiconformal mappings in $\IR^n$. As application, the quasisymmetry of quasiconformal mappings is discussed. 
M. Huang, Y. Li, S. Ponnusamy and X. Wang
math.CV