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arXiv · 0708.3025

The Green's function and the Ahlfors map

Steven R. Bell
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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.

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Steven R. Bell. 2007-08-22. The Green's function and the Ahlfors map. https://arxiv.org/abs/0708.3025

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