Abstract
This paper contributes to the theory of quasiextremal distance domains. We present some new properties for these domains and point out results concerning the extension of quasiconformal homeomorphisms.For example, we establish a continuity property for mod(E, F; D) and use this to demonstrate that mod(E, F; D) = cap(E, F; D) whenever D is a QED domain and E, F are disjoint compacta in D. Our final result is that if each boundary component of a plane domain is either a point or a Jordan curve and if the domain satisfies a boundary quasiextremal distance property, then there exists a quasiconformal self-homeomorphism of the entire plane which maps the given domain conformally onto a circle domain.
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