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Single-valued determination of closed surfaces of genus p≥1 in a space of constant curvature

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Abstract

We supply a proof of the single-valued determination of closed locally convex surfaces of genus p≥1 in a space of constant curvature with point type exterior connections.

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Literature cited

  1. 1.

    V. T. Fomenko, “On the rigidity and the single-valued determination of closed surfaces of genus p≥1 in a Riemannian space,” Dokl. Akad. Nauk SSSR,213, No. 1, 45–48 (1973).

  2. 2.

    V. T. Fomenko, “On the single-valued determination of ovaloids with cuts,” Dokl. Akad. Nauk SSSR,152, No. 6, 1320–1323 (1963).

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

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    A. I. Serbin, “On the Riemann boundary value problem for a generalized function on a closed Riemann surface,” Izv. Vuzov, Matematika, No. 4, 131–143 (1964).

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Additional information

Translated from Matematicheskie Zametki, Vol. 16, No. 3, pp. 441–445, September, 1974.

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Fomenko, V.T. Single-valued determination of closed surfaces of genus p≥1 in a space of constant curvature. Mathematical Notes of the Academy of Sciences of the USSR 16, 852–854 (1974). https://doi.org/10.1007/BF01148134

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Keywords

  • Constant Curvature
  • Closed Surface
  • Point Type
  • Type Exterior
  • Exterior Connection