Bounds on spherical derivatives for maps into regions with symmetries

  • Mario Bonk
  • William Cherry


  1. [A-G]
    S. B. Agard and F. W. Gehring,Angles and quasiconformal mappings, Proc. London Math. Soc. (3)14A (1965), 1–21.MathSciNetCrossRefGoogle Scholar
  2. [Ca]
    C. Carathéodory,Theory of Functions of a Complex Variable, Volume Two, Chelsea, New York, 1960.Google Scholar
  3. [Hej]
    D. Hejhal,Universal covering maps for variable regions, Math. Z.137 (1974), 7–20.MATHCrossRefMathSciNetGoogle Scholar
  4. [Hem]
    J. A. Hempel,The Poincaré metric on the twice punctured plane and the theorems of Landau and Schottky, J. London Math. Soc. (2)20 (1979), 435–445.MATHCrossRefMathSciNetGoogle Scholar
  5. [Ho]
    E. Hopf,A remark on linear elliptic differential equations of second order, Proc. Amer. Math. Soc.3 (1952), 791–793.MATHCrossRefMathSciNetGoogle Scholar
  6. [Je]
    J. A. Jenkins,On explicit bounds in Landau’s theorem II, Can. J. Math.33 (1981), 559–562.MATHMathSciNetGoogle Scholar
  7. [JØ]
    V. JØrgensen,On an inequality for the hyperbolic measure and its applications to the theory of functions, Math. Scand.4 (1956), 113–124.MATHMathSciNetGoogle Scholar
  8. [Mi1]
    D. Minda,Estimates for the hyperbolic metric, Kodai Math. J.8 (1985), 249–258.MATHCrossRefMathSciNetGoogle Scholar
  9. [Mi2]
    D. Minda,The hyperbolic metric and Bloch constants for spherically convex regions, Complex Variables5 (1986), 127–140.MATHMathSciNetGoogle Scholar
  10. [Mi3]
    D. Minda,A reflection principle for the hyperbolic metric and applications to geometric function theory, Complex Variables8 (1987), 129–144.MATHMathSciNetGoogle Scholar
  11. [M-O]
    D. Minda and M. Overholt,The minimum points of the hyperbolic metric, Complex Variables21 (1993), 265–277.MATHMathSciNetGoogle Scholar
  12. [Ne]
    Z. Nehari,Conformal Mapping, Dover, New York, 1952.MATHGoogle Scholar
  13. [P-W]
    M. H. Protter and H. Weinberger,Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967.Google Scholar
  14. [Ya]
    A. Yamada,Bounded analytic functions and metrics of constant curvature on Riemann surfaces, Kodai Math. J.11 (1988), 317–324.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 1996

Authors and Affiliations

  • Mario Bonk
    • 1
  • William Cherry
    • 2
  1. 1.Institut für AnalysisTech. Univ. BraunschweigBraunschweigGermany
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

Personalised recommendations