Generalized quasidisks and conformality II

Abstract

We introduce a weaker variant of the concept of three point property, which is equivalent to a non-linear local connectivity condition introduced by the author, Koskela, and Takkinen, sufficient to guarantee the extendability of a conformal map $f:\mathbb {D}\to \Omega$ to the entire plane as a homeomorphism of locally exponentially integrable distortion. Sufficient conditions for extendability to a homeomorphism of locally $p$-integrable distortion are also given.