Advertisement

Journal d’Analyse Mathématique

, Volume 69, Issue 1, pp 275–291 | Cite as

On Bloch’s constant

  • Huaihui Chen
  • Paul M. Gauthier
Article

Abstract

The well-known lower estimate for Bloch’s constantB is thatB > √3/4. Recently, M. Bonk has improved this estimate by showing thatB > √3/4 + 10-14. We give a further improvement by showing thatB ≥√3/4 + 2 × 10-14.

Keywords

Riemann Surface Unit Disk Nagoya Math Euclidian Length Bloch Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    L. V. Ahlfors,An extension of Schwarz’s lemma, Trans. Amer. Math. Soc.,43 (1938), 359–364.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    L. V. Ahlfors and H. Grunsky,über die Blochsche Konstante, Math. Z.42 (1937), 671–673.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    M. Bonk,On Bloch’s constant, Proc. Amer. Math. Soc.110 (1990), 889–894.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    M. Heins,On a class of conformal metrics, Nagoya Math. J.21 (1962), 1–60.zbMATHMathSciNetGoogle Scholar
  5. [5]
    E. Landau,über die Bloch’sche Konstante und zwei verwandte Weltkonstanten, Math. Z.30 (1929), 608–634.CrossRefMathSciNetzbMATHGoogle Scholar
  6. [6]
    C. D. Minda,Bloch constants, J. Analyse Math.41 (1982), 54–84.zbMATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Ch. Pommerenke,On Bloch functions, J. London Math. Soc.2 (1970), 689–695.zbMATHMathSciNetGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 1996

Authors and Affiliations

  • Huaihui Chen
    • 1
  • Paul M. Gauthier
    • 2
  1. 1.Department of MathematicsNanjing Normal UniversityNanjing, JiangsuP.R. China
  2. 2.Département de Mathématiques et de StatistiqueUniversité de MontréalMontréalCanada

Personalised recommendations