An Improvement of the Second Fundamental Theorem for Holomorphic Curves

  • Nobushige Toda
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 7)


Let f = [f 1,…, f n +1] be a linearly non-degenerate and transcendental holomorphic curve from C in to the n-dimensional complex projective space P n (C) with a reduced representation (f 1,…, f n +1): CC n +1 {0}, where n is a positive integer. In this paper, we use the same notation for f and for a vector a = (a 1, … a n +1) ∈ C n +1− {0} as in [6]:
$$\left\| {f(z)} \right\|,\left\| a \right\|,(a,f),(a,f(z)),T(r,f),m(r,a,f),N(r,a,f),\delta (a,f),S(r,f)etc$$




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  1. [1]
    H. Cartan: Sur les combinaisons linéaires de p fonctions holomorphes données. Mathematica 7 (1933), 5–31.MATHGoogle Scholar
  2. [2]
    W. Chen: Defect relations for degenerate meromorphic maps. Trans. Amer. Math. Soc., 319–2 (1990), 499–515.CrossRefGoogle Scholar
  3. [3]
    R. Nevanlinna: Le théorème de Picard-Borel et la théorie des fonctions méromorphes. Gauthier-Villars, Paris 1929.MATHGoogle Scholar
  4. [4]
    E. I. Nochka: On the theory of meromorphic functions. Soviet Math. Dokl., 27–2 (1983), 377–381.Google Scholar
  5. [5]
    N. Toda: On the fundamental inequality for non-degenerate holomorphic curves. Kodai Math. J., 20–3 (1997), 189–207.MathSciNetCrossRefGoogle Scholar
  6. [6]
    N. Toda: On the second fundamental inequality for holomorphic curves. Bull. of Nagoya Inst. of Tech., 50 (1998), 123–135.MathSciNetMATHGoogle Scholar

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© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Nobushige Toda
    • 1
  1. 1.Department of MathematicsNagoya Institute of TechnologyNagoyaJapan

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