SOME APPLICATIONS OF EXTREMAL LENGTH TO CONFORMAL IMBEDDINGS

Abstract

Let G be a Denjoy domain and let G' a Denjoy proper subdomain of G and homeomorphic to G. We consider conformal re-imbeddings of G' into G. Let G and G' are N -connected. We know that if N = 2, there is a re-imbedding f of G' into G such that G − cl(f (G')) has an interior point. In this note, we obtain the following theorem.

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