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Conformal pasting on a torus

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Abstract

We solve the problem concerning global conformal pasting on a torus given by the algebraic equation

$$u^2 = (1 - z^2 ) (1 - k^z 2^2 ) (0< k< 1).$$

We obtain an algebraic equation for the new torus, and we find the function which accomplishes the conformal pasting.

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Literature cited

  1. G. Springer, Introduction to the Theory of Riemann Surfaces, Addison-Wesley, Reading, Mass. (1957).

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  2. É. I. Zverovich, “Method of locally conformai pasting,” Dokl. Akad. Nauk SSSR,205, No. 4, 767–770 (1972).

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  4. É. I. Zverovich, “The Behnke-Stein kernel and the solution in closed form of the Riemann boundary value problem on the torus,” Dokl. Akad. Nauk SSSR,188, No. 1, 27–30 (1969).

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Authors and Affiliations

  1. Odessa Polytechnic Institute, USSR

    N. I. Zhukova

Authors
  1. N. I. Zhukova
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Additional information

Translated from Matematicheskie Zametki, Vol. 16, No. 1, pp. 83–90, July, 1974.

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Zhukova, N.I. Conformal pasting on a torus. Mathematical Notes of the Academy of Sciences of the USSR 16, 635–639 (1974). https://doi.org/10.1007/BF01098817

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  • DOI: https://doi.org/10.1007/BF01098817

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