The Picard theorem for Riemann surfaces

Royden, H. L.

doi:10.1090/S0002-9939-1984-0733408-6

The Picard theorem for Riemann surfaces
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by H. L. Royden

Proc. Amer. Math. Soc. 90 (1984), 571-574

DOI: https://doi.org/10.1090/S0002-9939-1984-0733408-6

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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 $0 < \left | z \right | < 1$ 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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