Skip to main content
SpringerLink
Log in

Extremal problems in a class of mappings with bounded integral characteristics

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

Abstract

We consider mappings with bounded integral characteristics. We construct extremal mappings of plane rings realizing the minimum of these characteristics.

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. P. P. Belinskii, General Properties of Quasiconformal Mappings [in Russian] Nauka, Novosibirsk 1974.

    Google Scholar 

  2. P. A. Biluta, “Certain extremal problems for mappings quasiconformal in the mean,” Sib. Mat. Zh., 6, No. 4, 717–726 1989.

    MathSciNet  Google Scholar 

  3. V. S. Kud’yavin and A. L. Gol’berg, “Mean coefficients of quasiconformality of a pair of domains,” Ukr. Mat. Zh., 43, No. 12, 1709–1712(1991).

    Google Scholar 

  4. A. V. Sychev, Moduli and Space Quasiconformal Mappings [in Russian] Nauka, Novosibirsk 1983.

    Google Scholar 

  5. A. L. Gol’berg, “On some classes of plane topological mappings with the generalized first derivatives,” Ukr. Mat. Zh., 44, No. 8, 1114–1116(1992).

    MathSciNet  Google Scholar 

  6. V. S. Kud’yavin, “A characteristic property of one class of space homeomorphisms,” Dokl Akad. Nauk Ukr. SSR, Ser. A, No. 3, 73–78(1990).

  7. W. P. Ziemer, “Extremal length and p-capacity,” Mich. Math. J., 16, 43–51 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  8. V. M. Gol’dshtein and Yu. G. Reshetnyak, Introduction to the Theory of Functions with Generalized Derivatives and Quasiconformal Mappings [in Russian] Nauka, Moscow 1983.

    Google Scholar 

  9. A. L. Gol’berg and V. S. Kud’yavin, “On one extremal mapping of plane annuli,” in: Complex Analysis and Potential Theory [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 23–26.

    Google Scholar 

  10. A. L. Gol’berg, “Extremal mappings of plane annuli and p-moduli,” in: Contemporary Problems in Approximation Theory and Complex Analysis [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1990), pp. 25–29.

    Google Scholar 

  11. J. Vaisala, Lectures on n-Dimensional Quasiconformal Mappings, Lect. Notes Math., Springer, Berlin (1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Crimean Institute for Protection of Nature and Resort Development, Simeropol

    A. L. Gol’berg

Authors
  1. A. L. Gol’berg
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gol’berg, A.L. Extremal problems in a class of mappings with bounded integral characteristics. Ukr Math J 52, 624–627 (2000). https://doi.org/10.1007/BF02515402

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02515402

Keywords

Search

Navigation