Koebe's general uniformisation theorem for planar Riemann surfaces

Volume 100 / 2011

Gollakota V. V. Hemasundar Annales Polonici Mathematici 100 (2011), 77-85 MSC: Primary 30F10. DOI: 10.4064/ap100-1-7


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 $\mathbb{C}$.


  • Gollakota V. V. HemasundarDepartment of Mathematics
    SIWS College
    Mumbai, India

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