Skip to main content
Log in

Tchebotaröv’s extremal problem

  • Published:
Central European Journal of Mathematics

Abstract

We give the complete solution of the extremal problem posed by N.G. Tchebotaröv in 20th of the last century, and we establish explicit parametric formulae for the extremals.

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. G.M. Golusin: “Method of variations in the theory of conform representation”, I, Mat. Sb., Vol. 19(61), (1946), pp. 203–236, (in Russian).

    MATH  MathSciNet  Google Scholar 

  2. G.M. Golusin: Geometric Theory of Functions of a complex Variable, AMS, Rhode Island, 1969 (transl. from Russian).

    Google Scholar 

  3. H. Grötzsch, “Über ein Variationsproblem der konformen Abbildung”, Ber. Ferch. Sächs. Akad. Wiss. Leipzig, Vol. 82, (1930), pp. 251–263.

    MATH  Google Scholar 

  4. J.A. Jenkins: Univalent functions and conformal mappings, Inostr. Lit, Moscow, 1962, (Russian transl.).

    Google Scholar 

  5. S.L. Krushkal, B.N. Apanasov and B.N. Gusevskii: Kleinian groups and uniformisation in examples and problems, Nauka, Novosibirsk, 1981, (in Russian).

    Google Scholar 

  6. G.V. Kuz’mina: “Covering theorems for functions holomorphic and univalent within a disk”, Dokl. Acad. Nauk SSSR, Vol. 160, (1965), pp. 25–28 (Russian.)

    MathSciNet  Google Scholar 

  7. M.A. Lavrentieff, “Sur un probleme de maximum dans la representation conforme”, C. R. Acad. Sci. Paris, Vol. 191, (1930), pp. 827–829.

    MATH  Google Scholar 

  8. M.A. Lavrentyev: “On the theory of conformal mappings”, Trudy Fiz-Mat. Inst. Akad. Nauk SSSR, Vol. 5, (1934), pp. 159–246, (in Russian).

    Google Scholar 

  9. R. Nevanlinna: Uniformisierung, Inostr. Lit., Moscow, 1955, (Russian transl.).

    MATH  Google Scholar 

  10. G. Polya: Beitrag zur Verallgemeinerung des Verzerrungssatzes auf mehrfach zusammenhängende Gebiete, III, S.-B. Preuss. Akad. Wiss, Berlin, 1929, pp. 55–62.

    Google Scholar 

  11. Ch. Pommerenke: Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975.

    MATH  Google Scholar 

  12. P.M. Tamrazov: “Theorems on the covering of lines under a conformal mapping”, Mat. Sb., Vol. 66(108), (1965), pp. 502–524 (Russian).

    MATH  MathSciNet  Google Scholar 

  13. P.M. Tamrazov: Tchebotaröv’s extremal problem, Kiev, 2004; (Prepr./National Acad. Sci. of Ukraine. Inst. of Math.; 2004.9).

  14. P. Tamrazov: “Tchebotaröv’s problem”, C. R. Acad. Sci. Paris, Ser. I, (to be published).

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Tamrazov, P.M. Tchebotaröv’s extremal problem. centr.eur.j.math. 3, 591–605 (2005). https://doi.org/10.2478/BF02475620

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.2478/BF02475620

Keywords

MSC (2000)

Navigation