Towards an Effectivisation of the Riemann Theorem

Abstract

Let Q be a connected and simply connected domain on the Riemann sphere, not coinciding with the Riemann sphere and with the whole complex plane ℂ. Then, according to the Riemann Theorem, there exists a conformal bijection between Q and the exterior of the unit disk. In this paper, we find an explicit form of this map for a broad class of domains with analytic boundaries.