Skip to main content
Log in

Certain extremal problems concerning module and harmonic measure

  • Published:
Journal d’Analyse Mathématique Aims and scope

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.

References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. T. Bagby,The modulus of a plane condenser, J. Math. Mech.17 (1967), 315–329.

    MATH  MathSciNet  Google Scholar 

  3. D. Gaier,Estimates of conformal mappings near the boundary, Indiana Univ. Math. J.21 (1972), 581–595.

    Article  MATH  MathSciNet  Google Scholar 

  4. H. Grötzsch,Über ein Variationsproblem der konkformen Abbildung, Ber. Verh. sächs, Akad. Wiss. Lipzig, Math.-phys. K1.82 (1930), 251–263.

    Google Scholar 

  5. J. A. Jenkins,On the existence of certain general extremal metrics, Ann. of Math., II. Ser.66 (1957), 440–453.

    Article  MathSciNet  Google Scholar 

  6. J. A. Jenkins,Univalent Functions and Conformal Mapping, Springer-Verlag, Berlin-Heidelberg-New York, 1965.

    Google Scholar 

  7. J. A. Jenkins,On a problem concerning harmonic measure, Math. Z.135 (1974), 279–283.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. G. Krzyż,An extremal length problem and its applications, Proceedings of the NRL Conference on Classical Function Theory, U.S. Government Printing Office, Washington, D.C., 1970, pp. 143–155.

  9. R. Kühnau,Geometrie der konformen Abbildung auf der hyperbolischen und der elliptischen Ebene, VEB Deutscher Verlag der Wissenschaften, Berlin, 1974.

    MATH  Google Scholar 

  10. G. V. Kuz’mina,On the conformal modulus in classes of doubly connected domains not containing given systems of points, Zap. Naučn. Sem. LOMI24 (1972), 78–147 (English translation in J. Soviet Math.2 (1974), 618–667).

    MathSciNet  MATH  Google Scholar 

  11. G. V. Kuz’mina,Estimates of the conformal modulus of a set of domains and covering theorems for univalent functions, Zap. Naučn. Sem. LOMI24 (1972), 148–172 (English translation in J. Soviet Math.2 (1974), 668–685).

    MathSciNet  Google Scholar 

  12. F. Leja,Sur les suites de polynômes, les ensembles fermés et la fonction de Green, Ann. Soc. Polon. Math.12 (1934), 57–71.

    MATH  Google Scholar 

  13. L. Liao,On a minimax formula of Leja’s, to appear in Kõdai Math. J.

  14. A. C. Schaeffer and D. C. Spencer,Coefficient regions for schlicht functions, Amer. Math. Soc. Colloquium Publ. 35, New York, 1950.

  15. O. Teichmüller,Extremale quasikonforme Abbildungen und quadratische Differentiale, Abh. preuss. Akad. Wiss., Phys.-Math. Kl. 1939, No. 22.

  16. M. Tsuji,Potential Theory in Modern Function Theory, Maruzen Co., Ltd., Tokyo, 1959.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liao, L. Certain extremal problems concerning module and harmonic measure. J. Anal. Math. 40, 1–42 (1981). https://doi.org/10.1007/BF02790155

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02790155

Keywords

Navigation