Skip to main content
SpringerLink
Log in

Moduli of continuity of exterior and interior conformal mappings of the unit disc

  • Published:
Ukrainian Mathematical Journal Aims and scope

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

Literature cited

  1. J. M. Anderson, K. F. Barth, and D. A. Brannan, “Research problems in complex analysis,” Bull. London Math. Soc,9, 129–162 (1977).

    Google Scholar 

  2. F. D. Lesley, “On interior and exterior conformal mappings of the disk,” J. London Math. Soc. (I),20, 67–78 (1979).

    Google Scholar 

  3. J. Becker and C. Pommerenke, “Hölder continuity of conformal mappings and nonquasicon-formal Jordan curves,” Commun. Math. Helv.,57, 221–225 (1982).

    Google Scholar 

  4. F. D. Lesley, “Conformal mappings of domains satisfying a wedge condition,” Proc. Am. Math. Soc,93, No. 3, 483–488 (1985).

    Google Scholar 

  5. D. Gaier, “Estimates of conformal mappings near the boundary,” Indiana Math. J.,27, No. 7, 581–595 (1972).

    Google Scholar 

  6. V. I. Belyi, “Local metric properties of a conformal map of a simply connected domain onto the exterior of the unit disc,” in: Metric Questions of the Theory of Functions and Mappings [in Russian], Naukova Dumka, Kiev (1975), pp. 17–32.

    Google Scholar 

  7. V. I. Belyi, “Conformal mappings and approximation of functions in domains with quasiconformal boundary,” Mat. Sb.,102, No. 3, 331–361 (1977).

    Google Scholar 

  8. V. I. Belyi, “Development of the method of conformal invariants and quasiconformal quasiinvariants from the view point of application to problems of polynomial approximation,” in: Approximation and Function Spaces: Proc. Int. Conf. (Gdansk, August 27–31, 1979), North-Holland, Amsterdam-New York-Oxford (1981), pp. 102–121.

    Google Scholar 

  9. P. M. Tamrazov, “Contour and solid properties of holomorphic functions of a complex variable,” Usp. Mat. Nauk,28, No. 1, 131–161 (1973).

    Google Scholar 

  10. V. I. Belyi, “Constants in estimates of distortion of distance under a conformal mapping,” Dokl. Rassh. Zased. Sem. Inst. Prikl. Mat. I. N. Vekua,1, No. 1, 36–39 (1985).

    Google Scholar 

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

    Google Scholar 

  12. L. Ahlfors, Lectures on Quasiconformal Mappings [Russian translation], Mir, Moscow (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    V. I. Belyi

Authors
  1. V. I. Belyi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 4, pp. 469–475, April, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belyi, V.I. Moduli of continuity of exterior and interior conformal mappings of the unit disc. Ukr Math J 41, 409–414 (1989). https://doi.org/10.1007/BF01060617

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01060617

Keywords

Search

Navigation