Abstract and Applied Analysis

Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks

Yu-Ming Chu

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Abstract

We prove that a homeomorphism f : R 2 → R 2 is a quasiconformal mapping if and only if f ( D ) is an arcwise connected domain for any arcwise connected domain D ⊆ R 2 , and D is a quasidisk if and only if both D and its exterior D * = R 2 ∖ 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

Permanent link to this document
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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