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16. References
Ahlfors, L. V.: The theory of meromorphic curves. Acta Soc. Sci. Fenn. Nova Ser A 3 (4) (1941), 1–31.
Biancofiore, A.: A hypersurface defect relation for a class of meromorphic maps. Trans. Amer. Math. Soc. 270 (1982), 47–60.
Biancofiore, A.: A defect relation for meromorphic maps. Manuscript.
Biancofiore, A.: A defect relation for linear systems on compact complex monifolds. Manuscript.
Biancofiore, A., Stoll W.: Another proof of the lemma of the logarithmic derivative in several complex variables, in "Recent developments in several complex variables". Annals of Math. Studies 100, Princeton University Press, Princeton, N. J. (1981), 29–45.
Borel, E.: Sur les zéros des fonctions entières. Acta Math. 20 (1897), 357–396.
Bott, R., Chern, S. S.: Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections. Acta Math. 114 (1965), 71–112.
Burns, D.: Curvature of Monge-Ampère foliations and parabolic manifolds. Manuscript.
Carlson J., Griffiths Ph.: A defect relation for equidimensional holomorphic mappings between algebraic varieties. Ann. of Math. 95 (1972), 557–584.
Cartan, H.: Un noveau théoreme d'unicité relatif aux fonctions méromorphes. C.R. Acad. Sci. 188 (1929), 301–303.
Cartan, H.: Sur les zéros des combinaisons linéaires des fonctions holomorphes données. Mathematica (Clnj) 7 (1933), 5–31.
Chern, S. S.: The integrated form of the first main theorem for complex analytic mappings in several variables, Ann. of Math. 77 (1960), 536–551.
Chern, S. S.: Holomorphic curves in the plane, in "Diff. Geom. in honor of K. Yano". Kinokuniya, Tokyo (1972), 72–94.
Cowen, M.: Hermitian vector bundles and value distribution for Schubert cycles. Trans. Amer. Math. Soc. 180 (1973), 189–228.
Cowen, M., Griffiths, Ph.: Holomorphic curves and metrics of negative curvature, J. Analyse Math. 29 (1976), 93–152.
Fujimoto, H.: The uniqueness problem of meromorphic maps into the complex projective space. Nagoya Math. J. 58 (1975), 1–23.
Fujimoto, H.: The uniqueness theorem of algebraically non-degenerate meromorphic maps into IPn (ℂ). Nagoya Math. J. 64 (1976), 117–147.
Fujimoto, H.: Remarks to the uniqueness problem of meromorphic maps I, III. Nagoya Math. J. 71 (1978) 13–41, 75 (1979) 71–85.
Fujimoto, H.: On the defect relation of the derived curves of a holomorphic curve in IPn (ℂ). Tôhoku Math. J. 34 (1982), 141–160.
Green, M.: Holomorphic maps into complex projective space omitting hyperplanes. Trans. Amer. Math. Soc. 169 (1972), 89–103.
Green, M.: Some Picard theorems for holomorphic maps to algebraic varieties. Amer. J. Math. 97 (1975), 43–75.
Green, M.: Some examples and counter-examples in value distribution theory for several variables. Compositio Math. 30 (1975), 317–322.
Griffiths, Ph.: Holomorphic mappings into canonical algebraic varieties. Ann. of Math. 93 (1971), 439–458.
Griffiths, Ph.: Holomorphic mappings: Survey of some results and discussion of open problems. Bull. Amer. Math. Soc. 78 (1972), 374–382.
Griffiths, Ph., King, J.: Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math. 130 (1973), 145–220.
Griffiths, Ph.: Entire holomorphic mappings in one and several complex variables. Annals of Math. Studies 85, Princeton University Press, Princeton, N. J. (1976).
Gruman, L.: Value distribution for holomorphic maps into ℂn. Math. Ann. 245 (1979), 29–37.
Gruman, L.: La geometrie globale des ensembles analytiques dans ℂn, in "Séminaire P. Lelong-H. Skoda (Analyse). Années 1978/79". Lecture Notes in Mathematics 822, Springer-Verlag, Berlin-Heidelberg-New York (1980), 90–98.
Hayman, W. K.: Meromorphic functions. Oxford University Press, Oxford (1964).
Hirschfelder, J.: The first main theorem of value distribution in several variables. Invent. Math. 8 (1969), 1–33.
Kataka Conference: Open problems in geometric function theory. Proceed. 5. Int. Symp. Division Math. The T niguchi Foundation (available from: Dept. of Math. Osaka Univ., Toyonaka, 560 Japan) (1978).
Kneser, H.: Zur Theorie der gebrochenen Funktionen mehrerer Veränderlichen. Jahresber. Deutsch. Math.-Verein. 48 (1938), 1–28.
Lelong, P.: Fonctions entiéres (n-variables) et fonctions plurisous-harmoniques d'ordre fini dans ℂn. J. Analyse Math. 12 (1964), 365–407.
Levine, H.: A theorem on holomorphic mappings into complex projective space. Ann. of Math. 71 (1960), 529–535.
Molzon, R. E.: Sets omitted by equidimensional holomorphic mappings Amer. J. Math. 101 (1979), 1271–1283.
Molzon, R. E., Shiffman, B., Sibony, N.: Average growth estimates for hyperplane sections of entire analytic sets. Math. Ann. 257 (1981), 43–59.
Mori, S.: On the deficiencies of meromorphic maps of ℂm into INN(ℂ). Nagoya Math. J. 67 (1977), 165–176.
Mori, S.: The deficiencies and the order of holomorphic mappings of ℂn into a compact complex manifold. Tôhoku Math. J. 31 (1979), 285–291.
Mori, S.: Holomorphic curves with maximal deficiency sum. Kodai Math. J. 2 (1979), 116–122.
Murray, J.: A second main theorem of value distribution theory on Stein manifolds with pseudoconvex exhaustion (1974). Notre Dame Thesis.
Nevanlinna, R.: Einige Eindeutigkeitssätze in der Theorie der meromorphen Funktionen. Acta Math. 48 (1926), 367–391.
Nevanlinna, R.: Eindeutige analytische Funktionen. 2. Auflage. Springer-Verlag, Berlin-Göttingen-Heidelberg (1953).
Noguchi, J.: A relation between order and defects of meromorphic mappings of ℂn into IPN(ℂ). Nagoya Math. J. 59 (1975), 97–106.
Noguchi, J.: Holomorphic curves in algebraic varieties. Hiroshima Math. J. 6 (1977), 833–853. Supplement: Hiroshima Math. J. 10 (1980), 229–231.
Noguchi, J., Sunada, T.: Finiteness of the family of rational and meromorphic mappings into algebraic varieties. Manuscript.
Ronkin, L. I.: Introduction to the theory of entire functions of several variables. Translations of Mathematical Monographs 44, Amer. Math. Soc., Providence, R. I. (1974).
Sadullaev, A.: Deficient divisors in the Valiron sense. Math USSR-Sb. 36 (1980), 535–547.
Sakai, F.: Degeneracy of holomorphic maps with ramification. Invent. Math. 26 (1974), 213–229.
Shiffman, B.: Holomorphic and meromorphic mappings and curvature. Math. Ann. 222 (1976), 171–194.
Shiffman, B.: Applications of geometric measure theory to value distribution theory for meromorphic maps, in "Value-Distribution Theory Part A", Marcel Dekker, Inc., New York (1974), 63–95.
Shiffman, B.: Nevanlinna defect relations for singular divisors. Invent. Math. 31 (1975), 155–182.
Shiffman, B.: Holomorphic curves in algebraic manifolds. Bull. Amer. Math. Soc. 83 (1977), 155–182.
Shiffman, B.: On holomorphic curves and meromorphic maps in projective space. Indiana Univ. Math. J. 28 (1979), 627–641.
Skoda, H.: Solution a croissance du second problème de Cousin dans ℂn. Ann. Inst. Fourier (Grenoble) 21 (1971), 11–23.
Skoda, H.: Sous-ensembles analytiques d'ordre fini ou infini dans ℂn. Bull. Soc. Math. France 100 (1972), 353–408.
Smiley, L.: Dependence theorems for meromorphic maps. (1979). Notre Dame Thesis.
Stoll, W.: Mehrfache Integrale auf komplexen Mannigfaltigkeiten. Math. Z. 57 (1952), 116–154.
Stoll, W.: Ganze Funktionen endlicher Ordnung mit gegebenen Nullstellenflächen. Math. Z. 57 (1953), 211–237.
Stoll, W.: Die beiden Hauptsätze der Wertverteilungstheorie bei Funktionen mehrerer komplexer Veränderlichen I, II. Acta Math. 90 (1953), 1–115, 92 (1954), 55–169.
Stoll, W.: The growth of the area of a transcendental analytic set I, II Math. Ann. 156 (1964), 47–78, 156 (1964), 144–170.
Stoll, W.: The multiplicity of a holomorphic map. Invent. Math. 2 (1966), 154–218.
Stoll, W.: A general first main theorem of value distribution. Acta Math. 118 (1967), 111–191.
Stoll, W.: About value distribution of holomorphic maps into projective space. Acta Math. 123 (1969), 83–114.
Stoll, W.: Value distribution of holovorphic maps into compact complex manifolds. Lecture Notes in Mathematics 135, Springer-Verlag, Berlin-Heidelberg-New York (1970).
Stoll, W.: Value distribution of holomorphic maps, in "Several complex variables I, Maryland 1970". Lecture Notes in Mathematics 155. Springer-Verlag, Berlin-Heidelberg-New York (1970), 165–170.
Stoll, W.: Fiber integration and some of its applications, in "Symposium on Several Complex Variables, Park City, Utah, 1970". Lecture Notes in Mathematics 184, Springer-Verlag, Berlin-Heidelberg-New York (1971), 109–120.
Stoll, W.: Deficit and Bezout estimates, in "Value — Distribution Theory Part B". Marcel Dekker, Inc., New York (1973).
Stoll, W.: Holomorphic functions of finite order in several complex variables. CBMS. Regional Conference Series in Mathematics 21, Amer. Math. Soc., Providence, R. I. (1974).
Stoll, W.: Aspects of value distribution theory in several complex variables. Bull. Amer. Math. Soc. 83 (1977), 166–183.
Stoll, W.: Value distribution theory on parabolic spaces. Lecture Notes in Mathematics 600, Springer-Verlag, Berlin-Heidelberg-New York (1977).
Stoll, W.: A Casorati — Weierstrass Theorem for Schubert zeroes in semi-ample holomorphic vector bundles. Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8) 15 (1978), 63–90.
Stoll, W.: The characterization of strictly parabolic manifolds. Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4) 7 (1980), 87–154.
Stoll, W.: The characterization of strictly parabolic spaces. Compositio Math. 44 (1981), 305–373.
Stoll, W.: Introduction to value distribution theory of meromorphic maps. To appear in Proceeding of the 1980 Trieste Conference, Lecture Notes in Mathematics, Springer-Verlag.
Sung, C. H.: On the deficiencies of holomorphic curves in projective space. Manuscript.
Tung, Ch.: The first main theorem of value distribution on complex spaces. Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (8) 15 (1979), 91–263.
Vitter, A.: The lemma of the logarithmic derivative in several complex variables. Duke Math. J. 44 (1977), 89–104.
Weyl, H., Weyl, J.: Meromorphic curves. Ann. of Math. 39 (1938), 516–538.
Weyl, H., Weyl, J.: Meromorphic functions and analytic curves. Annals of Math. Studies 12, Princeton University Press, Princeton, N. J. (1943).
Wirtinger, W.: Ein Integralsatz über analytische Gebilde im Gebiete von mehreren komplexen Veränderlichen. Monatshefte Math. Phys. 45 (1937), 418–431.
Wong, P.-M.: Defect relations for maps on parabolic spaces and Kobayashi metrics on projective spaces omitting hyperplanes. (1976) Notre Dame Thesis.
Wong, P.-M.: Geometry of the complex homogeneous Monge — Ampére equation. Invent. Math. 67 (1982), 261–274.
Wu, H.: Mappings of Riemann surfaces (Nevanlinna Theory). Proc. Sympos. Pure Math. 11 (1968), 480–552.
Wu, H.: Remarks on the first main teorem of equidistribution theory I–IV. J. Differential Geom. 2 (1968), 197–202 and 369–384, 3 (1969), 83–94 and 433–446.
Wu, H.: The equidistribution theory of holomorphic curves. Annals of Math. Studies 64, Princeton University Press, Princeton, N.J. (1970).
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Stoll, W. (1983). The ahlfors — Weyl theory of meromorphic maps on parabolic manifolds. In: Laine, I., Rickman, S. (eds) Value Distribution Theory. Lecture Notes in Mathematics, vol 981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066385
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