Article PDF
Avoid common mistakes on your manuscript.
Bibliography
Bieberbach, L., Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln. S.-B. preuss. Akad. Wiss. 138, 940–955 (1916).
Bombieri, E., On the local maximum of the Koebe function. Inventiones math. 4, 26–67 (1967).
Garabedian, P.R., An extension of Grunsky's inequalities bearing on the Bieberbach conjecture. J. d'Analyse Math. XVIII, 81–97 (1967).
Garabedian, P.R., G.G. Ross, & M. Schiffer, On the Bieberbach conjecture for even n. J. Math. Mech. 14, 975–989 (1965).
Garabedian, P.R., & M. Schiffer, A proof of the Bieberbach confecture for the fourth coefficient. J. Rational Mech. Anal. 4, 427–465 (1955).
Garabedian, P.R., & M. Schiffer, The local maximum theorem for the coefficients of univalent functions. Arch. Rational Mech. Anal. 26, 1–31 (1967).
Grunsky, H., Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen. Math. Z. 45, 29–61 (1939).
Jenkins, J., Some area theorems and a special coefficient theorem. Ill. J. Math. 8, 88–99 (1964).
Jenkins, J., & M. Ozawa, On local maximality for the coefficient a 6. Nagoya Math. J. 30, 71–88 (1967).
Kazdan, J., A boundary value problem arising in the theory of univalent functions. J. Math. Mech. 13, 283–303 (1964).
Loewner, K., Untersuchungen über schlichte konforme Abbildungen des Einkeitskreises I. Math. Ann. 89, 103–121 (1923).
Nehari, Z., Conformal Mapping. New York: McGraw Hill 1952.
Ozawa, M., On the sixth coefficient of univalent functions. Kodai Math. Seminar Reports 17, 1–9 (1965).
Pederson, R., A note on the local coefficient problem (to appear).
Pederson, R., On unitary properties of Grunsky's matrix (to appear in Arch. Rational Mech. Anal.).
Pederson, R., A numerical approach to the sixth coefficient problem. Carnegie-Mellon Univ. Technical Report 68-3.
Schaeffer, A.C., & D.C. Spencer, Coefficient regions for schlicht functions. Amer. Math. Soc. Colloquium Publ. 35, New York, 1950.
Schiffer, M., Univalent functions whose first n coefficients are real. J. d'Anal. Math. 18, 329–349 (1967).
Schiffer, M., & Z. Charzynski, A new proof of the Bieberbach conjecture for the fourth coefficient. Arch. Rational Mech. Anal. 5, 187–193 (1960).
Schiffer, M., & P. Duren, The theory of the second variation in extremum problems for univalent function. J. d'Anal. Math. 10, 193–252 (1962–63).
Schur, I., Ein Satz über quadratische Formen mit komplexen Koeffizienten. Amer. J. Math. 67, 472–480 (1945).
Author information
Authors and Affiliations
Additional information
Communicated by M. M. Schiffer
This research was supported by the National Science Foundation, Grant NSF GP-7662.
Rights and permissions
About this article
Cite this article
Pederson, R.N. A proof of the Bieberbach conjecture for the sixth coefficient. Arch. Rational Mech. Anal. 31, 331–351 (1968). https://doi.org/10.1007/BF00251415
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00251415