English

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}
}

Comments

14 pages

R2 v1 2026-06-21T09:09:42.127Z