Koebe's general uniformisation theorem for planar Riemann surfaces
Volume 100 / 2011
Annales Polonici Mathematici 100 (2011), 77-85
MSC: Primary 30F10.
DOI: 10.4064/ap100-1-7
Abstract
We give a complete and transparent proof of Koebe's General Uniformisation Theorem that every planar Riemann surface is biholomorphic to a domain in the Riemann sphere $\hat{\mathbb{C}}$, by showing that a domain with analytic boundary and at least two boundary components on a planar Riemann surface is biholomorphic to a circular-slit annulus in $\mathbb{C}$.
