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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Picard theorem for Riemann surfaces
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by H. L. Royden PDF
Proc. Amer. Math. Soc. 90 (1984), 571-574 Request permission

Abstract:

Let $W$ be a Riemann surface other than the sphere, plane, punctured plane or torus. Let $f$ be a holomorphic map of the punctured disk $0 < \left | z \right | < 1$ into $W$. Then $f$ can be extended to a holomorphic map of the disk $\left | z \right | < 1$, possibly, into a Riemann surface ${W^ * }$ containing $W$. We give a new proof of this fact and explore some consequences of it.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 571-574
  • MSC: Primary 30F35; Secondary 30F99
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0733408-6
  • MathSciNet review: 733408