Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks

Abstract EN

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.