Aspects of value distribution theory in several complex variables
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- by Wilhelm Stoll PDF
- Bull. Amer. Math. Soc. 83 (1977), 166-183
References
- Lars V. Ahlfors, The theory of meromorphic curves, Acta Soc. Sci. Fennicae. Nova Ser. A 3 (1941), no. 4, 31. MR 4309
- 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
- Raoul Bott and Shiing S. Chern, Some formulas related to complex transgression, Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), Springer, New York, 1970, pp. 48–57. MR 0264715
- 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
- Shiing-shen Chern, The integrated form of the first main theorem for complex analytic mappings in several complex variables, Ann. of Math. (2) 71 (1960), 536–551. MR 125979, DOI 10.2307/1969943
- Michael J. Cowen, Hermitian vector bundles and value distribution for Schubert cycles, Trans. Amer. Math. Soc. 180 (1973), 189–228. MR 333252, DOI 10.1090/S0002-9947-1973-0333252-5
- Mark L. Green, Holomorphic maps into complex projective space omitting hyperplanes, Trans. Amer. Math. Soc. 169 (1972), 89–103. MR 308433, DOI 10.1090/S0002-9947-1972-0308433-6
- Phillip A. Griffiths, Holomorphic mapping into canonical algebraic varieties, Ann. of Math. (2) 93 (1971), 439–458. MR 281954, DOI 10.2307/1970883
- Phillip A. Griffiths, Function theory of finite order on algebraic varieties. I(B), J. Differential Geometry 7 (1972), 45–66. MR 325999
- 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
- Phillip A. Griffiths, Entire holomorphic mappings in one and several complex variables, Annals of Mathematics Studies, No. 85, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976. The fifth set of Hermann Weyl Lectures, given at the Institute for Advanced Study, Princeton, N. J., October and November 1974. MR 0447638, DOI 10.1515/9781400881482
- 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
- John J. Hirschfelder, The first main theorem of value distribution in several variables, Invent. Math. 8 (1969), 1–33. MR 245840, DOI 10.1007/BF01418868
- John J. Hirschfelder, On Wu’s form of the first main theorem of value distribution, Proc. Amer. Math. Soc. 23 (1969), 548–554. MR 247597, DOI 10.1090/S0002-9939-1969-0247597-5 15. H. Kneser, Zur Theorie der gebrochenen Funktionen mehrerer Veränderlichen, Jber, Deutsch. Math.-Verein 48 (1938), 1-28.
- Pierre Lelong, Fonctions entières ($n$ variables) et fonctions plurisousharmoniques d’ordre fini dans $C^{n}$, J. Analyse Math. 12 (1964), 365–407 (French). MR 166391, DOI 10.1007/BF02807441
- Harold I. Levine, A theorem on holomorphic mappings into complex projective space, Ann. of Math. (2) 71 (1960), 529–535. MR 117757, DOI 10.2307/1969942
- Yozo Matsushima, On a problem of Stoll concerning a cohomology map from a flag manifold into a Grassmann manifold, Osaka Math. J. 13 (1976), no. 2, 231–269. MR 418134 19. J. Murray, A second main theorem of value distribution theory on Stein manifolds with pseudoconvex exhaustion, Thesis, Notre Dame, 1974, pp. 1-69.
- Rolf Nevanlinna, Eindeutige analytische Funktionen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band XLVI, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1953 (German). 2te Aufl. MR 0057330, DOI 10.1007/978-3-662-06842-7 21. W. Stoll, Die beiden Hauptsätze der Wertverteilungstheorie bie Funktionen mehrerer komplexer Veränderlichen. I, II, Acta Math. 90 (1953), 1-115; ibid. 92 (1954), 55-169. MR 17 #893, 894.
- Wilhelm Stoll, A general first main theorem of value distribution. I, Acta Math. 118 (1967), 111–146. MR 217339, DOI 10.1007/BF02392479
- Wilhelm Stoll, About the value distribution of holomorphic maps into the projective space, Acta Math. 123 (1969), 83–114. MR 259173, DOI 10.1007/BF02392386
- 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, DOI 10.1007/BFb0059118
- Wilhelm Stoll, Value distribution of holomorphic maps, Several Complex Variables, I (Proc. Conf., Univ. of Maryland, College Park, Md., 1970) Springer, Berlin, 1970, pp. 165–190. MR 0269881
- Robert O. Kujala (ed.), Value-distribution theory, Part B, Pure and Applied Mathematics, vol. 25, Marcel Dekker, Inc., New York, 1973. MR 0344509
- Wilhelm Stoll, High points in the history of value distribution theory of several complex variables, Proceedings Symposium on Value Distribution Theory in Several Complex Variables (Notre Dame, IN, 1990) Notre Dame Math. Lectures, vol. 12, Univ. Notre Dame Press, Notre Dame, IN, 1992, pp. 1–36. MR 1243016
- Wilhelm Stoll, A Casorati-Weierstrass theorem for Schubert zeroes of semi-ample holomorphic vector bundles, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8) 15 (1978), no. 3, 63–90 (English, with Italian summary). MR 531918 29. Ch. Tung, The first main theorem on complex spaces, Thesis, Notre Dame, 1973, pp. 1-320.
- Hermann Weyl, Meromorphic Functions and Analytic Curves, Annals of Mathematics Studies, No. 12, Princeton University Press, Princeton, N. J., 1943. MR 0009057 31. P. Wong, Defect relations for meromorphic maps from parabolic manifolds into complex projective spaces, Thesis, Notre Dame, 1976, pp. 1-231.
- H. Wu, Remarks on the first main theorem in equidistribution theory. I, J. Differential Geometry 2 (1968), 197–202. MR 276500
- 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, DOI 10.1007/BF02392435
Additional Information
- Journal: Bull. Amer. Math. Soc. 83 (1977), 166-183
- MSC (1970): Primary 32H25, 32H99; Secondary 32F99
- DOI: https://doi.org/10.1090/S0002-9904-1977-14247-X
- MathSciNet review: 0427692