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

TL;DR

This paper resolves a long-standing open problem by proving the subinvariance of John domains under quasiconformal mappings in n and explores implications for quasisymmetry of these mappings.

Contribution

It provides a complete solution to Heinonen's 1989 open problem on subinvariance of John domains under quasiconformal maps in n.

Findings

Proves subinvariance of John domains under quasiconformal mappings in n

Establishes conditions for quasisymmetry of quasiconformal maps

Completes the theoretical understanding of domain invariance properties

Abstract

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.