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Proceedings of the American Mathematical Society

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Continuation of Riemann surfaces


Author: Richard Rochberg
Journal: Proc. Amer. Math. Soc. 48 (1975), 82-86
MSC: Primary 30A30; Secondary 30A46
DOI: https://doi.org/10.1090/S0002-9939-1975-0396927-5
MathSciNet review: 0396927
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Abstract: It is known that a nonplanar Riemann surface cannot be continued into all compact Riemann surfaces of a fixed positive genus. The Poincaré metric is used to construct a conformal invariant which is used to give an essentially geometric proof of this result.


References [Enhancements On Off] (What's this?)

  • [1] L. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand Math. Studies, no. 10, Van Nostrand, Princeton, N.J., 1966. MR 34 #336. MR 0200442 (34:336)
  • [2] M. Heins, A problem concerning the continuation of Riemann surfaces, Contributions to the Theory of Riemann Surfaces, Ann. of Math. Studies, no. 30, Princeton Univ. Press, Princeton, N.J., 1953, pp. 55-62. MR 15, 25. MR 0056097 (15:25b)
  • [3] H. Rauch, A transcendental view of the space of algebraic Riemann surfaces, Bull. Amer. Math. Soc. 71 (1965), 1-39. MR 35 #4403. MR 0213543 (35:4403)
  • [4] C. L. Siegel, Topics in complex function theory, Vols. I, II, Wiley, New York, 1971. MR 1008930 (90h:30002)
  • [5] J. Jenkins, On a result of M. Heins (to appear). MR 0387575 (52:8415)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0396927-5
Article copyright: © Copyright 1975 American Mathematical Society

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