Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
MathSciNet review:
1567534
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
Peter L. Duren
Title:
Univalent functions
Additional book information:
Grundlehren der mathematischen Wissenschaften 259, Springer-Verlag, New York, 1983, $46.00, xiv + 382 pp. ISBN 0-3879-0795-5.
Lars V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand Mathematical Studies, No. 10, D. Van Nostrand Co., Inc., Toronto, Ont.-New York-London, 1966. Manuscript prepared with the assistance of Clifford J. Earle, Jr. MR 0200442
Lars V. Ahlfors, Conformal invariants: topics in geometric function theory, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0357743
Lars V. Ahlfors, Quasiconformal mappings, Teichmüller spaces, and Kleinian groups, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 71–84. MR 562598
Lars Valerian Ahlfors, Collected papers. Vol. 1, Contemporary Mathematicians, Birkhäuser, Boston, Mass., 1982. 1929–1955; Edited with the assistance of Rae Michael Shortt. MR 688648
Albert Baernstein II, How the $\ast$-function solves extremal problems, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 639–644. MR 562666
Albert Baernstein II, Bieberbach’s conjecture for tourists, Harmonic analysis (Minneapolis, Minn., 1981) Lecture Notes in Math., vol. 908, Springer, Berlin-New York, 1982, pp. 48–73. MR 654179
Albert Baernstein II and Juan J. Manfredi, Topics in quasiconformal mapping, Topics in modern harmonic analysis, Vol. I, II (Turin/Milan, 1982) Ist. Naz. Alta Mat. Francesco Severi, Rome, 1983, pp. 819–862. MR 748884
Lipman Bers, Uniformization, moduli, and Kleinian groups, Bull. London Math. Soc. 4 (1972), 257–300. MR 348097, DOI 10.1112/blms/4.3.257
Lipman Bers, Finite-dimensional Teichmüller spaces and generalizations, Bull. Amer. Math. Soc. (N.S.) 5 (1981), no. 2, 131–172. MR 621883, DOI 10.1090/S0273-0979-1981-14933-8
Peter L. Duren, Coefficients of univalent functions, Bull. Amer. Math. Soc. 83 (1977), no. 5, 891–911. MR 470182, DOI 10.1090/S0002-9904-1977-14324-3
F. W. Gehring, Some metric properties of quasi-conformal mappings, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 203–206. MR 0432875
F. W. Gehring, Spirals and the universal Teichmüller space, Acta Math. 141 (1978), no. 1-2, 99–113. MR 499134, DOI 10.1007/BF02545744
13. F. W. Gehring, Review of [18], Bull Amer. Math. Soc. (N.S.) 3 (1980), 1062-1064.
Frederick W. Gehring, Characteristic properties of quasidisks, Séminaire de Mathématiques Supérieures [Seminar on Higher Mathematics], vol. 84, Presses de l’Université de Montréal, Montreal, Que., 1982. MR 674294
F. W. Gehring, Injectivity of local quasi-isometries, Comment. Math. Helv. 57 (1982), no. 2, 202–220. MR 684113, DOI 10.1007/BF02565857
A. W. Goodman, Univalent functions. Vol. I, Mariner Publishing Co., Inc., Tampa, FL, 1983. MR 704183
D. H. Hamilton, Extremal boundary problems, Proc. London Math. Soc. (3) 56 (1988), no. 1, 101–113. MR 915532, DOI 10.1112/plms/s3-56.1.101
Samuil L. Krushkal′, Quasiconformal mappings and Riemann surfaces, A Halsted Press Book, V. H. Winston & Sons, Washington, D.C.; John Wiley & Sons, New York-Toronto, Ont.-London, 1979. Edited by Irvin Kra [Irwin Kra]; Translated from the Russian; With a foreword by Lipman Bers. MR 536488
O. Lehto and K. I. Virtanen, Quasiconformal mappings in the plane, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 126, Springer-Verlag, New York-Heidelberg, 1973. Translated from the German by K. W. Lucas. MR 0344463
Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768
Glenn Schober, Univalent functions—selected topics, Lecture Notes in Mathematics, Vol. 478, Springer-Verlag, Berlin-New York, 1975. MR 0507770
- 1.
- L. V. Ahlfors, Lectures on quasiconformal mappings, Van Nostrand, Princeton, N. J., 1966. MR 0200442
- 2.
- L. V. Ahlfors, Conformal invariants, McGraw-Hill, New York, 1973. MR 357743
- 3.
- L. V. Ahlfors, Quasiconformal mappings, Teichmüller spaces, and Kleinian groups, Proc. Internat. Congress Math. (Helsinki, 1978), Vol. 1, Academia Scientiarum Fennica, 1980, pp. 71-84. MR 562598
- 4.
- L. V. Ahlfors, Collected papers, Vols. 1, 2, Birkhaüser, Boston, 1982. MR 688648
- 5.
- A. Baernstein, How the *-function solves extremal problems, Proc. Internat. Congress Math. (Helsinki, 1978), Vol. 2, pp. 639-644. MR 562666
- 6.
- A. Baernstein, Bieberbach's conjecture for tourists, Harmonic Analysis (Proc Conf., Minneapolis, 1981), Lecture Notes in Math., vol. 908, Springer-Verlag, Berlin, 1982. MR 654179
- 7.
- A. Baernstein, Topics in quasiconformal mappings, Topics in Modern Harmonic Analysis (Proc. Conf. Milano, 1982), L. de Michele and F. Ricci, eds., Istituto Nazionale di Alta Matematica Francesco Sevani, Roma, 1983. MR 748884
- 8.
- L. Bers, Uniformization, moduli, and Kleinian groups, Bull. London Math. Soc. 4 (1972), 257-300. MR 348097
- 9.
- L. Bers, Finite dimensional Teichmüller spaces, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 131-172. MR 621883
- 10.
- P. L. Duren, Coefficients of univalent functions, Bull. Amer. Math. Soc. 83 (1977), 891-909. MR 470182
- 11.
- F. W. Gehring, Some metric properties of quasi-conformal mappings, Proc. Internat. Congress Math. (Vancouver, 1974), Vol. 2, Canadian Math. Congress, 1975, pp. 203-207. MR 432875
- 12.
- F. W. Gehring, Spirals and the universal Teichmüller space, Acta Math. 141 (1978), 99-113. MR 499134
- 13.
- F. W. Gehring, Review of [18], Bull Amer. Math. Soc. (N.S.) 3 (1980), 1062-1064.
- 14.
- F. W. Gehring, Characteristic properties of quasidisks, Les Presses Univ. Montréal, Montreal, 1982. MR 674294
- 15.
- F. W. Gehring, Injectivity of local quasi-isometries, Comment. Math. Helv. 57 (1982), 202-220. MR 684113
- 16.
- A. W. Goodman, Univalent functions, Vols. I, II, Mariner, Tampa, 1983. MR 704183
- 17.
- D. H. Hamilton, Extremal boundary problems for Schlicht functions, preprint, Univ. of Maryland, 1984. MR 915532
- 18.
- S. L. Krushkal, Quasiconformal mappings and Riemann surfaces, V. H. Winston, Washington, D. C., 1979. MR 536488
- 19.
- O. Lehto and K. I. Virtanen, Quasiconformal mappings in the plane, 2nd ed. Springer-Verlag, Berlin, 1973. MR 344463
- 20.
- Ch. Pommerenke, Univalent functions, Vandenheock and Ruprecht, Göttingen, 1975. MR 507768
- 21.
- G. Schober, Univalent functions-selected topics, Lecture Notes in Math., vol. 478, Springer-Verlag, Berlin, 1975. MR 507770
Review Information:
Reviewer:
Albert Baernstein, II
Journal:
Bull. Amer. Math. Soc.
12 (1985), 158-165
DOI:
https://doi.org/10.1090/S0273-0979-1985-15330-3
