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

  Published:2016-09-16
 Printed: Dec 2016
  • Paul M Gauthier,
    Département de mathématiques et de statistique, Université de Montréal, CP-6128 Centreville, Montréal H3C3J7
  • Fatemeh Sharifi,
    Department of Mathematics, Middlesex College, The University of Western Ontario, London, Ontario N6A 5B7
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Abstract

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: bordered Riemann surface, reflection principle, Osgood-Carathéodory bordered Riemann surface, reflection principle, Osgood-Carathéodory
MSC Classifications: 30C25, 30F99 show english descriptions Covering theorems in conformal mapping theory
None of the above, but in this section
30C25 - Covering theorems in conformal mapping theory
30F99 - None of the above, but in this section
 

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