The Uniformization Theorem

University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

Author: Nikita Zozoulenko; [2021]

Keywords: complex analysis; riemann surface; analytic functions; holomorphic functions; differential geometry; harmonic; subharmonic; perron; analysis; Mathematics and Statistics;

Abstract: In this bachelor's thesis we provide a self contained proof of the Uniformization Theorem. It states that a simply connected Riemann surface is conformally equivalent to either the complex plane C, the unit disk D, or the Riemann sphere C^'. The proof given in this thesis is purely analytic and is based on the construction of Green's function and bipolar Green's function of a Riemann surface through the Perron method.

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