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Continuations of Riemann Surfaces

Published online by Cambridge University Press:  20 November 2018

Makoto Sakai
Makoto Sakai*
Affiliation:
Tokyo Metropolitan University Tokyo, Japan
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Abstract

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We shall show that if a Riemann surface is continuable, then it admits one of three types of continuations. Using this classification of continuations, we construct two nontrivial examples of two-sheeted unlimited covering Riemann surfaces of the unit disk one of which is continuable and the other is not.

Keywords

Primary:30F20secondary:30F15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 2 , 01 April 1992 , pp. 357 - 367
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Bochner, S., Fortsetzung Riemannscher Flächen, Math. Ann., 98(1928), 406–421.Google Scholar
2. Jurchescu, N., Bordered Riemann surfaces, Math. Ann., 143(1961), 264–292.Google Scholar
3. Lehto, O. and Virtanen, K.I., QuasiconformalMapping in the Plane, Sec. Ed. Springer-Verlag, Berlin, 1973.Google Scholar
4. Oikawa, K., Riemann Surfaces, to be translated from Japanese into English.Google Scholar
5. Radó, T., Über eine nicht fortsetzbare Riemannsche Mannigfaltigkeit, Math. Z., 20(1924), 1–6.Google Scholar
6. Renggli, H., Structural instability and extensions of Riemann surfaces, Duke Math. J., 42(1975), 211–224.Google Scholar
7. Sakai, M., On the vanishing of the span of a Riemann surface, Duke Math. J., 41(1974), 497–510.Google Scholar
8. Sario, L. and Oikawa, K., Capacity Functions, Springer-Verlag, Berlin, 1969.Google Scholar
9. Shiba, M., The Riemann-Hurwitz relation, parallel slit covering map, and continuation of an open Riemann surface of finite genus, Hiroshima Math. J., 14(1984), 371–399.Google Scholar
10. Tamura, J., On a theorem of T suji, Japan J. Math., 29(1959), 138–140..Google Scholar