拟共形映射和弱Cigar域

Quasiconformal Mappings and Weakly Cigar Domains

中文关键词:  拟共形映射  弱Cigar域  弱拟凸域.

英文关键词:quasiconformal mapping  weakly Cigar domain  weakly quasiconvex domain.

中文摘要:

      设$f$是$R^n$到$R^n$上的同胚,本文证明了$f$是拟共形映射的充要条件是$f$将$R^n$中的任一弱Cigar域映成$R^n$中的弱Cigar域.

英文摘要:

      Let $f$: $R^n\rightarrow R^n$ be a homeomorphism. We prove that $f$ is a quasiconformal mapping if and only if the weakly Cigar domains in $R^n$ are invariant under $f$.