Generalized quasidisks

We say that a  Jordan domain in R^2  is a quasidisk if it is the image of the unit disk under a quasiconformal mapping of the entire plane. There are two equivalent geometric characterizations of a quasidisk, one is Ahlfors' three point property and the other is the so-called linear local connectivity. A generalized quasidisk is obtained in a similar fashion by replacing the globally quasiconformal mapping with a mapping of the plane from a wilder class: mappings of finite distortion with suitable control on the distortion function. We weaken the above-mentioned geometric concepts to determine when a Jordan domain is a generalized quasidisk. Connections with generalized John domains and uniform continuity of quasiconformal mappings will be discussed.