The Green's function and the Ahlfors map
Complex Variables
2009-09-29 v1
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.
Keywords
Cite
@article{arxiv.0708.3025,
title = {The Green's function and the Ahlfors map},
author = {Steven R. Bell},
journal= {arXiv preprint arXiv:0708.3025},
year = {2009}
}
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14 pages