Book Review
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MathSciNet review:
1566986
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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).
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.
Lars Ahlfors, Zur Theorie der Überlagerungsflächen, Acta Math. 65 (1935), no. 1, 157–194 (German). MR 1555403, DOI 10.1007/BF02420945
Lars V. Ahlfors, The theory of meromorphic curves, Acta Soc. Sci. Fennicae. Nova Ser. A 3 (1941), no. 4, 31. 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.
Emile Borel, Sur les zéros des fonctions entières, Acta Math. 20 (1897), no. 1, 357–396 (French). MR 1554885, DOI 10.1007/BF02418037
6. E. Borel, Leçons sur les fonctions entières, 2nd ed., Gauthier-Villars, Paris, 1921.
Raoul 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 185607, DOI 10.1007/BF02391818
James Carlson and Phillip Griffiths, A defect relation for equidimensional holomorphic mappings between algebraic varieties, Ann. of Math. (2) 95 (1972), 557–584. MR 311935, DOI 10.2307/1970871
9. H. Cartan, Sur les zéros des combinaisons linéaires de p fonctions holomorphes données, Mathematica (Cluj) 7 (1933), 5-31.
Shiing-shen Chern, Complex analytic mappings of Riemann surfaces. I, Amer. J. Math. 82 (1960), 323–337. MR 115183, DOI 10.2307/2372738
S. S. Chern, Complex manifolds without potential theory, Van Nostrand Mathematical Studies, No. 15, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0225346
I. M. Dektjarev, Problems of value distribution in dimensions higher than one, Uspehi Mat. Nauk 25 (1970), no. 6(156), 53–84 (Russian). MR 0316753
Albert Edrei, Sums of deficiencies of meromorphic functions, J. Analyse Math. 14 (1965), 79–107. MR 180678, DOI 10.1007/BF02806380
A. A. Gol′dberg and I. V. Ostrovskiĭ, Raspredelenie znacheniĭ meromorfnykh funktsiĭ, Izdat. “Nauka”, Moscow, 1970 (Russian). MR 0280720
Phillip A. Griffiths, Holomorphic mappings: Survey of some results and discussion of open problems, Bull. Amer. Math. Soc. 78 (1972), 374–382. MR 294718, DOI 10.1090/S0002-9904-1972-12905-7
Phillip A. Griffiths, Differential geometry and complex analysis, Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 2, Stanford Univ., Stanford, Calif., 1973) Amer. Math. Soc., Providence, R.I., 1975, pp. 43–64. MR 0399521
Phillip Griffiths, Some remarks on Nevanlinna theory, Value distribution theory (Proc. Tulane Univ. Program, Tulane Univ., New Orleans, La., 1972-1973) Dekker, New York, 1974, pp. 1–11. MR 0352545
Michael Cowen and Phillip Griffiths, Holomorphic curves and metrics of negative curvature, J. Analyse Math. 29 (1976), 93–153. MR 508156, DOI 10.1007/BF02789977
Phillip Griffiths and James King, Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math. 130 (1973), 145–220. MR 427690, DOI 10.1007/BF02392265
W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038
Rolf Nevanlinna, Zur Theorie der Meromorphen Funktionen, Acta Math. 46 (1925), no. 1-2, 1–99 (German). MR 1555200, DOI 10.1007/BF02543858
22. R. Nevanlinna, Le théorème de Picard-Borel et la theorie des fonctions meromorphes, Gauthier-Villars, Paris, 1929.
Rolf Nevanlinna, Analytic functions, Die Grundlehren der mathematischen Wissenschaften, Band 162, Springer-Verlag, New York-Berlin, 1970. Translated from the second German edition by Phillip Emig. MR 0279280
Bernard Shiffman, Holomorphic curves in algebraic manifolds, Bull. Amer. Math. Soc. 83 (1977), no. 4, 553–568. MR 440075, DOI 10.1090/S0002-9904-1977-14323-1
Wilhelm Stoll, Die beiden Hauptsätze der Wertverteilungstheorie bei Funktionen mehrerer komplexer Veränderlichen. I, Acta Math. 90 (1953), 1–115 (German). MR 76407, DOI 10.1007/BF02392435
Wilhelm Stoll, Value distribution of holomorphic maps into compact complex manifolds. , Lecture Notes in Mathematics, Vol. 135, Springer-Verlag, Berlin-New York, 1970. MR 0267138
Wilhelm Stoll, Aspects of value distribution theory in several complex variables, Bull. Amer. Math. Soc. 83 (1977), no. 2, 166–183. MR 427692, DOI 10.1090/S0002-9904-1977-14247-X
Al Vitter, The lemma of the logarithmic derivative in several complex variables, Duke Math. J. 44 (1977), no. 1, 89–104. MR 432924
R. O. Wells Jr., Differential analysis on complex manifolds, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1973. MR 0515872
Hermann Weyl, Meromorphic Functions and Analytic Curves, Annals of Mathematics Studies, No. 12, Princeton University Press, Princeton, N. J., 1943. MR 0009057
Hung-hsi Wu, The equidistribution theory of holomorphic curves, Annals of Mathematics Studies, No. 64, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0273070
- 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