The quasiconformal invariant properties of John domains in $\protect \IR^n$

Details The quasiconformal invariant properties of John domains in $\protect \IR^n$ The quasiconformal invariant properties of John domains in $\protect \IR^n$

2011-08-29

arxiv.org/abs/1108.5550v1

Mathematics

Complex Variables

45 pages, submitted to a journal

Scientific paper

Suppose that $D$ is a proper domain in $\IR^n$ and that $f$ is a quasiconformal mapping from $D$ onto a John domain $D'$ in $\IR^n$. The main aim of this paper is to prove that if $D_1\subset D$ is a John domain, then the image $f(D_1)$ of $D_1$ under $f$ is still a John domain. This result shows that the answer to one of the open problems raised by Heinonen in \cite{H} is affirmative.

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