This is a preview of subscription content, log in via an institution to check access.
References
L. V. Ahlfors,An extension of Schwarz's lemma, Trans. Am. Math. Soc.43 (1938), 359–364.
L. V. Ahlfors,Comformal Invariants. Topics in Geometric Function Theory, McGraw-Hill, New York, 1973.
L. V. Ahlfors and H. Grunsky,Über die Blochsche Konstante, Math. Z.42 (1937), 671–673.
C. Carathéodory,Theory of Functions, Vol. I, 2nd ed., Chelsea, New York, 1958.
C. Carathéodory,Theory of Functions, Vol. II, 2nd ed., Chelsea, New York, 1960.
G. M. Goluzin,Geometric theory of functions of a complex variable, Translations of Mathematical Monographs, Vol. 26, Am. Math. Soc., Providence, 1969.
R. E. Greene and H. Wu,Bloch's theorem for meromorphic functions, Math. Z.116 (1970), 247–257.
M. Heins,On a class of conformal metrics, Nagoya Math. J.21 (1962), 1–60.
V. Jørgensen,A remark on Bloch's theorem, Mat. Tidsskr. B. 1952 (1952), 100–103.
E. Landau,Der Picard-Schottkysche Satz und die Blochsche Konstante, Sitzungsber. Preuss. Akad. Wiss. Berlin, Phys.-Math. Kl. (1926), 467–474.
E. Landau,Über die Blochsche Konstante und zweis verwandte Weltkonstanten, Math. Z.30 (1929), 608–634.
C. D. Minda,The hyperbolic metric and coverings of Riemann surfaces, Pacific J. Math.84 (1979), 171–182.
C. D. Minda,Euclidean, hyperbolic and spherical Bloch constants, Bull. Am. Math. Soc.6 (1982), 441–444.
C. D. Minda,Bloch constants for meromorphic functions, Math. Z., to appear.
E. Peschl,Über die Verwendung von Differentialinvarienten bei gewissen Funktionenfamilien und die Übertragung einer darauf gegründeten Methode auf partielle Differentialgleichungen vom elliptische Typus, Ann. Acad. Sci. Fenn. Ser. AI No. 336/6 (1963), 23 pp.
E. Peschl,Über unverzweigte konforme Abbildungen, Österreich. Akad. Wiss. Math.-Naturwiss. Kl. S-B. II185 (1976), 55–78.
Ch. Pommerenke,Estimates for normal meromorphic functions, Ann. Acad. Sci. Fenn. Ser. AI, no. 476 (1970), 10p.
Ch. Pommerenke,On Bloch functions, J. London Math. Soc. (2)2 (1970), 689–695.
Ch. Pommerenke,Normal functions, Proc. NRL Conf. on Classical Function Theory, Math. Res. Center, Naval Res. Lab., Washington, D. C., 1970.
R. M. Robinson,Bloch constants, Duke Math. J.2 (1936), 453–459.
H. L. Royden,Real Analysis, 2nd ed., Macmillan, New York, 1968.
D. Stegenga and K. Stephenson,A geometric characterization of analytic functions with bounded mean oscillation, J. London Math. Soc. (2)24 (1981), 243–254.
M. Tsuji,On an extension of Bloch's theorem, Proc. Imp. Acad. Jpn.18 (1942), 170–171.
M. Tsuji,Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959.
Author information
Authors and Affiliations
Additional information
To Professor S. E. Warschawski on his 78th birthday.
This research was completed while the author was visiting the University of California, San Diego during 1980–81.
Rights and permissions
About this article
Cite this article
Minda, C.D. Bloch constants. J. Anal. Math. 41, 54–84 (1982). https://doi.org/10.1007/BF02803394
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02803394