Skip to main content
SpringerLink
Log in

Explicit relations for the reduced module and harmonic measure

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Exact relations are established for the reduced modules of the families of curves separating certain connected subsets in arbitrary connected domains. New explicit expressions for the harmonic measure of a connected boundary subset are obtained as corollaries.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. V. K. Dzyadyk,Introduction to the Theory of Uniform Approximations of Functions by Polynomials [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. V. I. Belyi, “Conformai mappings and approximation of analytic functions in the regions with quasiconformal boundary,”Mat. Sb.,102 (144), No. 3, 331–336 (1977).

    Google Scholar 

  3. V. I. Belyi, “Development of the method of conformai invariants and quasiconformal quasi-invariants from the viewpoint of application to problems of polynomial approximation,” in:Approximation and Function Spaces, North Holland, Amsterdam-Oxford-New York (1981), pp. 102–121.

    Google Scholar 

  4. V. I. Belyi, “On the constants in the estimates of distance distortion under conformal mappings,” in:Dokl. Rasshir. Sem. Im. Vekua,1, No. 1, 36–39 1985).

    Google Scholar 

  5. G. M. Goluzin,Geometrical Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  6. O. Teichmüller, “Untersuchungen über konforme und quasikonforme Ablildung,”Deutsch. Math.,3, 621–678 (1983).

    Google Scholar 

  7. L. V. Ahlfors andA. Beurling, “Conformal invariants and function theoretic null-sets,”Acta Math. 83, 101–129 (1950).

    Google Scholar 

  8. J. Hersch, “Longueurs extrémales et théorie des fonctions,”Com. Math. Helv.,29, 301–337 (1955).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    V. I. Belyi & E. V. Kravchuk

Authors
  1. V. I. Belyi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. V. Kravchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 576–578, April, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belyi, V.I., Kravchuk, E.V. Explicit relations for the reduced module and harmonic measure. Ukr Math J 45, 625–628 (1993). https://doi.org/10.1007/BF01062956

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01062956

Keywords

Search

Navigation