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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A general conformal geometric reflection principle
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by Oliver Roth PDF
Trans. Amer. Math. Soc. 359 (2007), 2501-2529 Request permission

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 $f$.
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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