IUMJ

Title: The Green's function and the Ahlfors map

Authors: Steven R. Bell

Issue: Volume 57 (2008), Issue 7, 3049-3064

Abstract:

The classical Green's function associated to a simply connected domain in the complex plane is easily expressed in terms of a Riemann mapping function. The purpose of this paper is to express the Green's function of a finitely connected domain in the plane in terms of a single Ahlfors mapping of the domain, which is a proper holomorphic mapping of the domain onto the unit disc that is the analogue of the Riemann map in the multiply connected setting.