Abstract:

Let D R² be a Jordan domain, D* = R² \ D, the exterior of D. In this article, the authors obtained the following results: (1) If D is a John disk, then D is an outer linearly locally connected domain; (2) If D* is a John disk, then D is an inner linearly locally connected domain; (3) A homeomorphism f : R²→ R² is a quasiconformal mapping if and only if f(D) is a John disk for any John disk D R²; and (4) If D is a bounded quasidisk, then D is a John disk, and there exists an unbounded quasidisk which is not a John disk.

Key words: John disks, Linearly locally connected domains, Quasiconformal mappings,
Quasidisks