References
C. Carathéodory,Über die Studysche Rundungsschranke, Math. Ann.79 (1919), 402.
F. W. Gehring,Spirals and the universal Teichmüller space, Acta Math.141 (1978), 99–113.
H. W. Guggenheimer,Differential Geometry, McGraw-Hill, New York, 1963.
E. Hopf,A remark on linear elliptic differential equations of second order, Proc. Amer. Math. Soc.3 (1952), 791–793.
V. Jorgensen,On an inequality for the hyperbolic measure and its applications to the theory of functions, Math. Scand.4 (1956), 113–124.
C. D. Minda,Lower bounds for the hyperbolic metric in convex regions, Rocky Mtn. J. Math.13 (1983), 61–69.
D. Minda,The hyperbolic metric and Bloch constants for spherically convex regions, Complex Variables Theory Appl.5 (1986), 127–140.
D. Minda,A reflection principle for the hyperbolic metric and applications to geometric function theory, Complex Variables Theory Appl.8 (1987), 129–144.
E. Netanyahu,The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1, Arch. Rational Mech. Anal.32 (1969), 100–112.
B. Osgood,Some properties of f″/f′ and the Poincaré metric, Indiana Univ Math. J.31 (1982), 449–461.
M. H. Protter and H. Weinberger,Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, N. J., 1967.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Minda, D. Applications of hyperbolic convexity to euclidean and spherical convexity. J. Anal. Math. 49, 90–105 (1987). https://doi.org/10.1007/BF02792893
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02792893