Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Phillip A. Griffiths
Title: Entire holomorphic mappings in one and several complex variables
Additional book information: Ann. of Math. Studies, no. 85, Princeton Univ. Press, Princeton, N. J., 1976, x + 99 pp., $11.50 (cloth) and $4.50 (paper).

References [Enhancements On Off] (What's this?)

  • 1. L. V. Ahlfors, Über eine Methode in der Theorie der Theorie der meromorphen Funktionen, Soc. Sci. Fenn. Comment. Phy.-Math. 8 (1935), 1-14.
  • 2. L. V. Ahlfors, Zur Theorie der Überlagerungsflächen, Acta Math. 65 (1935), 157-194. MR 1555403
  • 3. L. V. Ahlfors, The theory of meromorphic curves, Acta Soc. Sci. Fennicae. Nova Ser A 3 (1941), no. 4, 3-31. MR 2, 357. MR 4309
  • 4. E. Borel, Demonstration élémentaire d'un théorème de M. Picard sur les fonctions entières, C. R. Acad. Sci. 122 (1896), 1045-1048.
  • 5. E. Borel, Sur les zèroes des fonctions entières, Acta Math. 20 (1897), 357-396. MR 1554885
  • 6. E. Borel, Leçons sur les fonctions entières, 2nd ed., Gauthier-Villars, Paris, 1921.
  • 7. R. Bott and S. S. Chern, Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections, Acta Math. 114 (1965), 71-112. MR 32 #3070. MR 185607
  • 8. J. Carlson and P. Griffiths, A defect relation for equidimensional holomorphic mappings between algebraic varieties, Ann. of Math. (2) 95 (1972), 557-584. MR 47 #497. MR 311935
  • 9. H. Cartan, Sur les zéros des combinaisons linéaires de p fonctions holomorphes données, Mathematica (Cluj) 7 (1933), 5-31.
  • 10. S.-S. Chern, Complex analytic mappings of Riemann surfaces. I, Amer. J. Math. 82 (1960), 323-337. MR 22 #5985. MR 115183
  • 11. S.-S. Chern, Complex manifolds without potential theory, Van Nostrand, Princeton, N. J., 1967. MR 37 #940. MR 225346
  • 12. I. M. Dektjarev, Problems of value distribution in dimensions higher than one, Uspehi Mat. Nauk 25 (1970), no. 6 (156), 53-84 = Russian Math. Surveys 25 (1970), 51-82. MR 47 #5301. MR 316753
  • 13. A. Edrei, Sums of deficiencies of meromorphic functions, J. Analyse Math. 14 (1965), 79-107. MR 31 #4909. MR 180678
  • 14. A. A. Gold'berg and I. V. Ostrovskiĭ, The distribution of values of meromorphic functions, Izdat. "Nauka", Moscow, 1970. (Russian) MR 43 #6439. MR 280720
  • 15. P. A. Griffiths, Holomorphic mappings: Survey of some results and discussion of open problems, Bull. Amer. Math. Soc. 78 (1972), 374-382. MR 45 #3786. MR 294718
  • 16. P. A. Griffiths, Differential geometry and complex analysis, Proc. Sympos. Pure Math., vol. 27, Part II, Amer. Math. Soc. Providence, R. I., 1975, pp. 43-64. MR 399521
  • 17. P. A. Griffiths, Some remarks on Nevanlinna theory, Value Distribution Theory, Part A (R. Kujala and A. Vitter, editors), Dekker, New York, 1974, pp. 1-11. MR 50 #5032. MR 352545
  • 18. P. Griffiths and M. Cowen, Holomorphic curves and metrics of negative curvature, J. Analyse Math. 19 (1976), 93-153. MR 508156
  • 19. P. Griffiths and J. King, Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math. 130 (1973), 145-220. MR 427690
  • 20. W. K. Hayman, Meromorphic functions, Oxford Math. Monographs, Clarendon Press, Oxford, 1964. MR 29 # 1337. MR 164038
  • 21. R. Nevanlinna, Zur Theorie der meromorphen Funktionen, Acta Math. 46 (1925), 1-99. MR 1555200
  • 22. R. Nevanlinna, Le théorème de Picard-Borel et la theorie des fonctions meromorphes, Gauthier-Villars, Paris, 1929.
  • 23. R. Nevanlinna, Analytic functions, Springer-Verlag, Berlin and New York, 1970. MR 43 #5003. MR 279280
  • 24. B. Shiffman, Holomorphic curves in algebraic manifolds, Bull. Amer. Math. Soc. (to appear). MR 440075
  • 25. W. Stoll, Die beiden Hauptsätze der Wertverteilungstheorie bei Funktionen mehrer komplexer Veränderlichen. I, II, Acta Math. 90 (1953), 1-115; ibid. 92 (1954), 55-169. MR 17, 893. MR 76407
  • 26. W. Stoll, Value distribution of holomorphic maps into compact complex manifolds, Lecture Notes in Math., vol. 135, Springer-Verlag, Berlin and New York, 1970. MR 42 #2040. MR 267138
  • 27. W. Stoll, Aspects of value distribution theory in several complex variables, Bull. Amer. Math. Soc. 83 (1977), 166-183. MR 427692
  • 28. A. Vitter, The Lemma of the logarithmic derivative in several complex variables (to appear). MR 432924
  • 29. R. Wells, Differential analysis on real and complex manifolds, Prentice-Hall, Englewood Cliffs, N. J., 1973. MR 515872
  • 30. H. Weyl, Meromorphic functions and analytic curves, Ann. of Math. Studies, no. 12, Princeton Univ. Press, Princeton, N. J., 1943. MR 5, 94. MR 9057
  • 31. H. Wu, The equidistribution theory of holomorphic curves, Ann. of Math. Studies, no. 64, Princeton Univ. Press, Princeton, N. J., 1970. MR 42 #7951. MR 273070

Review Information:

Reviewer: David Drasin
Journal: Bull. Amer. Math. Soc. 83 (1977), 942-946
DOI: https://doi.org/10.1090/S0002-9904-1977-14330-9
American Mathematical Society