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Transactions of the American Mathematical Society

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Defect relations for degenerate meromorphic maps


Author: Wan Xi Chen
Journal: Trans. Amer. Math. Soc. 319 (1990), 499-515
MSC: Primary 32H30; Secondary 30D35, 32H25
DOI: https://doi.org/10.1090/S0002-9947-1990-1010882-9
MathSciNet review: 1010882
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Abstract: Using a concept called subgeneral position and adapting a weight function created by E. I. Nochka, this work proves the Cartan's conjecture on defect relations for a degenerate meromorphic map from a parabolic manifold into a projective space.


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

  • [1] H. Cartan, Sur les zéros des combinaisons linéaires de $ p$ fonctions holomorphes donnés, Mathematica (Cluj) 7 (1933), 80-103.
  • [2] W. Chen, Cartan's conjecture: defect relations for meromorphic maps from parabolic manifold to projective space, Ph.D. dissertation, Notre Dame University, 1987.
  • [3] -, On subgeneral position, Notre Dame Math. Preprints, #100, 1987.
  • [4] E. I. Nochka, Defect relations of meromorphic curves, Izv. Akad. Nauk Moldav. SSR Ser. Fiz.-Tekn. Mat. Nauk 1982, no. 1, 41-47. MR 672395 (84g:32039)
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  • [6] W. Stoll, The Ahlfors-Weyl theory of meromorphic maps on parabolic manifolds, Lecture Notes in Math., vol. 981, Springer-Verlag, 1983, pp. 101-219. MR 699135 (85c:32045)
  • [7] -, Value distribution theory of meromorphic maps, Aspects of Mathematics, E7, Vieweg, 1985. MR 823236 (88e:32038)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-1010882-9
Keywords: Value distribution, defect relations, degenerate, subgeneral position
Article copyright: © Copyright 1990 American Mathematical Society

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