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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A general conformal geometric reflection principle


Author: Oliver Roth
Journal: Trans. Amer. Math. Soc. 359 (2007), 2501-2529
MSC (2000): Primary 30A99; Secondary 30F45
DOI: https://doi.org/10.1090/S0002-9947-07-03942-6
Published electronically: January 4, 2007
MathSciNet review: 2286042
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a generalization of the Schwarz-Carathéodory reflec- tion principle for analytic maps $ f$ from the unit disk into arbitrary Riemann surfaces equipped with a complete real analytic conformal Riemannian metric $ \lambda(w) \, \vert dw\vert$. This yields a necessary and sufficient condition for $ f$ to have an analytic continuation in terms of the pullback of the metric $ \lambda(w) \, \vert dw\vert$ under the map $ f$.


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Additional Information

Oliver Roth
Affiliation: Mathematisches Institut, Universität Würzburg, D–97074 Würzburg, Germany
Email: roth@mathematik.uni-wuerzburg.de

DOI: https://doi.org/10.1090/S0002-9947-07-03942-6
Received by editor(s): January 20, 2005
Published electronically: January 4, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.