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Riemann Surfaces$
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Riemann Surfaces

Simon Donaldson

Print publication date: 2011

Print ISBN-13: 9780198526391

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780198526391.001.0001

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The Uniformisation Theorem

The Uniformisation Theorem

Chapter:
(p.131) 10 The Uniformisation Theorem
Source:
Riemann Surfaces
Author(s):

Simon Donaldson

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198526391.003.0010

This chapter proves the following theorem. Theorem 12: Let X be a connected, simply connected, non-compact Riemann surface. Then X is equivalent to either C or the upper half-plane H. The proof presented here follows the same general pattern as one already given to classify compact simply connected Riemann surfaces, but the non-compactness will require some extra steps.

Keywords:   Theorem 12, Riemann surface, proof, theorems

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