Geodesic
Koebe's general uniformisation theorem for planar Riemann surfaces
Gollakota V. V. Hemasundar1
1 Department of Mathematics SIWS College Mumbai, India
Annales Polonici Mathematici, Tome 100 (2011) no. 1, pp. 77-85

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\mathbb{C}$.
DOI : 10.4064/ap100-1-7
Keywords: complete transparent proof koebes general uniformisation theorem every planar riemann surface biholomorphic domain riemann sphere hat mathbb showing domain analytic boundary least boundary components planar riemann surface biholomorphic circular slit annulus mathbb

Gollakota V. V. Hemasundar 1

1 Department of Mathematics SIWS College Mumbai, India 
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Gollakota V. V. Hemasundar. Koebe's general uniformisation theorem for planar Riemann surfaces. Annales Polonici Mathematici, Tome 100 (2011) no. 1, pp. 77-85. doi: 10.4064/ap100-1-7

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