Extremal Length Decomposition and Domain Constants for Finitely Connected Domains

This paper is concerned with the study of quasi-extremal distance domains, a class of domains introduced by Gehring and Martio in connection with the theory of quasiconformal mappings. We obtain a sharp upper bound for the quasi-extremal distance constant (Formula presented.) of a finitely connected planar domain in terms of local boundary dilatation of its boundary components. For the proof of the main theorem, several independently interesting results are also established. One of them is a decomposition lemma about the extremal length of a curve family.