## Abstract and Applied Analysis

### Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks

Yu-Ming Chu

#### Abstract

We prove that a homeomorphism $f:{R}^{2}\to {R}^{2}$ is a quasiconformal mapping if and only if $f(D)$ is an arcwise connected domain for any arcwise connected domain $D\subseteq {R}^{2}$, and $D$ is a quasidisk if and only if both $D$ and its exterior ${D}^{\mathrm{\ast}}={R}^{2}\setminus \overline{D}$ are arcwise connected domains.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 419850, 5 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412279399

Digital Object Identifier
doi:10.1155/2014/419850

Mathematical Reviews number (MathSciNet)
MR3256246

Zentralblatt MATH identifier
07022359

#### Citation

Chu, Yu-Ming. Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 419850, 5 pages. doi:10.1155/2014/419850. https://projecteuclid.org/euclid.aaa/1412279399

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