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Proceedings of the American Mathematical Society

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

 

 

The Picard theorem for Riemann surfaces


Author: H. L. Royden
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
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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\vert z \right\vert < 1$ into $ W$. Then $ f$ can be extended to a holomorphic map of the disk $ \left\vert z \right\vert < 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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DOI: https://doi.org/10.1090/S0002-9939-1984-0733408-6
Article copyright: © Copyright 1984 American Mathematical Society