Remarks on John disks

Let be a Jordan domain, , 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.