Skip to main content
Log in

Moduli of multiply-connected domains on a Riemannian Mobius strip

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We investigate the modulus problem for families of curves in multiply-connected nonorientable domains on a Riemannian Mobius strip. We determine the extremal metric and the modulus of a “cross” family of arcs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. M. Tamrazov, Method of Extremal Metrics and Conformal Mappings [in Russian], Candidate-Degree Thesis (Physics and Mathematics), Kiev (1963).

  2. P. M. Tamrazov, “On some extremal problems in the theory of conformal mappings,” Mat. Sb., 109, No. 3. 329–337 (1965).

    MathSciNet  Google Scholar 

  3. P. M. Tamrazov, “Conformally invariant moduli and circular symmetrization.” in: Metric Problems in the Theory of Functions and Mappings [in Russian], Naukova Dumka. Kiev (1974), pp. 127–146.

    Google Scholar 

  4. P. M. Tamrazov, “Methods for investigation of extremal metrics and moduli of families of curves on a twisted Riemannian manifold,” Mat. St., 183, No. 3, 55–75 (1992).

    MATH  Google Scholar 

  5. P. M. Tamrazov, “Moduli and extremal metrics on nonorientable and twisted Riemannian manifolds,” Ukr. Mat. Zh., 50, No. 10. 1388–1398 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  6. P. M. Tamrazov, “Moduli and extremal metrics on twisted Riemannian manifolds,” in: Moduli of Nonorientable and Twisted Riemannian Manifolds [in Russian], Preprint No. 9, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1997), pp. 1–25.

  7. J.A. Jenkins, Univalent Functions and Conformal Mapping, Springer, Berlin 1958.

    MATH  Google Scholar 

  8. H. Grotzsch, “Das Kreissbogenschlitztheorem der konformen Abbildung mehrfach zusammenhangender schlichter Bereiche. I,” Leipzig. Ber., 83, No. 4, 238–253 (1931).

    Google Scholar 

  9. P. M. Tamrazov and S. A. Okhrimenko, “Pairwise products of moduli of families of curves on a Riemannian Mobius strip,” Ukr. Mat. Zh., 51, No. 1, 110–116 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  10. S. A. Okhrimenko and P. M. Tamrazov, “Estimates of products of moduli of families of curves on a Riemannian Mobius strip,” in: Moduli of Nonorientable and Twisted Riemannian Manifolds [in Russian], Preprint No. 9, Institute of Mathematics. Ukrainian Academy of Sciences, Kiev (1997), pp. 26–40.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Okhrimenko, S.A. Moduli of multiply-connected domains on a Riemannian Mobius strip. Ukr Math J 52, 407–412 (2000). https://doi.org/10.1007/BF02513135

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02513135

Keywords

Navigation