We prove that a homeomorphism is a quasiconformal mapping if and only if is an arcwise connected domain for any arcwise connected domain , and is a quasidisk if and only if both and its exterior are arcwise connected domains.
"Arcwise Connected Domains, Quasiconformal Mappings, and Quasidisks." Abstr. Appl. Anal. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/419850