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Pederson, R.; Schiffer, M.

A proof of the Bieberbach conjecture for the fifth coefficient. (English) Zbl 0241.30025

Arch. Ration. Mech. Anal. 45, 161-193 (1972).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 10 Documents

MSC:

30C50 Coefficient problems for univalent and multivalent functions of one complex variable
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[1] Bieberbach, L., Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln. S.-B. Preuss. Akad. Wiss. 1916, p. 940-955. · JFM 46.0552.01
[2] Bombieri, E., On the local maximum of the Koebe Function. Invent. Math. 4, 26-67 (1967). · Zbl 0174.12301 · doi:10.1007/BF01404579
[3] Charzynski, Z., & M. Schiffer, A new proof of the Bieberbach conjecture for the fourth coefficient. Arch. Rational Mech. Anal. 5, 187-193 (1960). · Zbl 0099.05901 · doi:10.1007/BF00252902
[4] Garabedian, P. R., Inequalities for the fifth coefficient. Comm. Pure. Appl. Math. 19, 199-214 (1966). · Zbl 0141.26902 · doi:10.1002/cpa.3160190206
[5] Garabedian, P. R., & M. Schiffer, A proof of the Bieberbach conjecture for the fourth coefficient. J. Rational Mech. Anal. 4, 427-465 (1955). · Zbl 0065.06902
[6] Garabedian, P. R., G. G. Ross, & M. Schiffer, On the Bieberbach conjecture for even n. J. Math. Mech. 14, 975-989 (1965). · Zbl 0141.26901
[7] Garabedian, P. R., & M. Schiffer, The local maximum theorem for the coefficients of univalent functions. Arch. Rational Mech. Anal. 26, 1-32 (1967). · Zbl 0174.12302 · doi:10.1007/BF00283856
[8] Grunsky, H., Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen. Math. Z. 45, 29-61 (1939). · JFM 65.0339.04 · doi:10.1007/BF01580272
[9] Jenkins, J. A., Some area theorems and a special coefficient theorem. Illinois J. Math. 8, 88-99 (1964). · Zbl 0131.07601
[10] Loewner, K., Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. Math. Ann. 89, 103-121 (1923). · JFM 49.0714.01 · doi:10.1007/BF01448091
[11] Milin, I. M., The area method in the theory of univalent functions. Dokl. Acad. Nauk SSSR 154, 264-267 (1964). · Zbl 0146.10205
[12] Ozawa, M., On the Bieberbach conjecture for the sixth coefficient. Kodai Math. Sem. Rep. 21, 97-128 (1969). · Zbl 0184.10502 · doi:10.2996/kmj/1138845834
[13] Pederson, R., On unitary properties of Grunsky’s matrix. Arch. Rational Mech. Anal. 29, 370-377 (1968). · Zbl 0182.41101 · doi:10.1007/BF00283900
[14] Pederson, R., A proof of the Bieberbach conjecture for the sixth coefficient. Arch. Rational Mech. Anal. 31, 331-351 (1968). · Zbl 0184.10501 · doi:10.1007/BF00251415
[15] Pederson, R., & M. Schiffer, Further generalizations of the Grunsky inequalities. J. Analyse Math. 23, 353-380 (1970). · Zbl 0212.42303 · doi:10.1007/BF02795509
[16] Pommerenke, Ch., Über die Faberschen Polynome schlichter Funktionen. Math. Z. 85, 197-208 (1964). · Zbl 0138.29901 · doi:10.1007/BF01112141
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