A general conformal geometric reflection principle
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- by Oliver Roth PDF
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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 $\lambda (w) |dw|$. This yields a necessary and sufficient condition for $f$ to have an analytic continuation in terms of the pullback of the metric $\lambda (w) |dw|$ under the map $f$.References
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Additional Information
- Oliver Roth
- Affiliation: Mathematisches Institut, Universität Würzburg, D–97074 Würzburg, Germany
- MR Author ID: 644146
- Email: roth@mathematik.uni-wuerzburg.de
- Received by editor(s): January 20, 2005
- Published electronically: January 4, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2286042