Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks - Yu-Ming Chu (Abstract and Applied Analysis)
We prove that a homeomorphism f:R2→R2 is a quasiconformal mapping if and only if f(D) is an arcwise connected domain for any arcwise connected domain D⊆R2, and D is a quasidisk if and only if both D and its exterior D*=R2∖D¯ are arcwise connected domains.