The Green's function and the Ahlfors map Steven Bell 30C35Szego kernel 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. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3454 10.1512/iumj.2008.57.3454 en Indiana Univ. Math. J. 57 (2008) 3049 - 3064 state-of-the-art mathematics http://iumj.org/access/