Quasiconformal Mappings and Plump Domains
拟共形映射和Plump域

Let $f: R^n\to R^n$ be a homeomorphism, in this paper, it is proved that$f$ is a $K$-quasiconformal mappings if and only if for any $c\geq1$, there exists $c^*\geq1$ such that $f$ maps any $c$-Plump domain onto $c^*$-Plump domain, where $c^*=c^*(n,K,c)$ is a constant depending only on $n,K$ and $c$ in the necessity, and $K=K(n,c,c^*)$ is a constant depending only on $n,c$ and $c^*$ in the sufficiency.