Domains bounded by analytic Jordan curves

Abstract

I t is well known that repeated application of the Riemann mapping theorem shows that any finitely connected plane domain is conformally equivalent to a domain whose boundary components are analytic curves. A corresponding result has not previously been shown for arbitrary domains of infinite connectivity—the only cases being those domains for which the Koebe conjecture is known to be true (cf. [2]). We will show that any domain with countably many boundary components is conjormally equivalent to a domain bounded by analytic Jordan curves and points.