Geodesic
The Carathéodory Reflection Principle and Osgood–Carathéodory Theorem on Riemann Surfaces
Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 776-793

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DOI

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.
DOI : 10.4153/CMB-2016-051-1
Mots-clés : 30C25, 30F99, bordered Riemann surface, reflection principle, Osgood-Carathéodory 
Gauthier, Paul M.; Sharifi, Fatemeh. The Carathéodory Reflection Principle and Osgood–Carathéodory Theorem on Riemann Surfaces. Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 776-793. doi: 10.4153/CMB-2016-051-1
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     author = {Gauthier, Paul M. and Sharifi, Fatemeh},
     title = {The {Carath\'eodory} {Reflection} {Principle} and {Osgood{\textendash}Carath\'eodory} {Theorem} on {Riemann} {Surfaces}},
     journal = {Canadian mathematical bulletin},
     pages = {776--793},
     year = {2016},
     volume = {59},
     number = {4},
     doi = {10.4153/CMB-2016-051-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-051-1/}
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