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The Carathéodory Reflection Principle and Osgood–Carathéodory Theorem on Riemann Surfaces

Published online by Cambridge University Press:  20 November 2018

Paul M. Gauthier  and
Fatemeh Sharifi
Paul M. Gauthier
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, CP-6128 Centreville, Montréal, QC, H3C 3J7 e-mail: gauthier@dms.umontreal.ca
Fatemeh Sharifi
Affiliation:
Department of Mathematics, Middlesex College, University of Western Ontario, London, ON, N6A 5B7 e-mail: fsharif8@uwo.ca
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Abstract

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The Osgood–Carathéodory theorem asserts that conformal mappings between Jordan domains extend to homeomorphisms between their closures. For multiply-connected domains on Riemann surfaces, similar results can be reduced to the simply-connected case, but we find it simpler to deduce such results using a direct analogue of the Carathéodory reflection principle.

Keywords

30C2530F99bordered Riemann surfacereflection principleOsgood-Carathéodory
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 4 , 01 December 2016 , pp. 776 - 793
Copyright
Copyright © Canadian Mathematical Society 2016

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