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A Difference Analogue of Cartan’s Second Main Theorem for Meromorphic Mappings

  • Real and Complex Analysis
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Abstract

In this paper, we prove a difference analogue of Cartan’s second main theorem for a meromorphic mapping on ℂm intersecting a finite set of fixed hyperplanes in general position on ℙn(ℂ). As an application, we prove a uniqueness theorem for a class of holomorphic curves by inverse images of n + 4 hyperplanes. This result is so far the best result about the uniqueness problem for holomorphic curves by inverse images of hyperplanes.

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References

  1. T.B. Cao, R. Korhonen, “A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables”, J. Math. Anal. Appl., 444(2), 1114–1132, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  2. H. Cartan, “Sur les zeros des combinaisions linearires de p fonctions holomorpes donnees”, Mathematica (Cluj), 7, 80–103, 1933.

    Google Scholar 

  3. Z. Chen, Q. Yan, “A note on uniqueness problem for meromorphic mapping with 2N + 3 hyperplanes”, Sci. China. Math, 53(10), 2657–2663, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Dethloff, T.V. Tan, “Uniqueness theorems for meromorphic mappings with few hyperplanes”, Bull. Sci. Math., 133, 501–514, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Fujimoto, “Value distribution theory of the Gauss map of minimal surfaces in Rm”, Aspects of Mathematics E21: Vieweg, 1993.

    Google Scholar 

  6. R. Halburd, R. Korhonen, “Difference analogue of the lemma on the logarithmic derivative with applications to difference equations”, J. Math. Anal. Appl., 314, 477–487, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Halburd, R. Korhonen, “Nevanlinna theory for the difference operator”, Ann. Acad. Sci. Fenn. Math., 31, 463–478, 2006.

    MathSciNet  MATH  Google Scholar 

  8. R. Halburd, R. Korhonen, K. Tohge, “Holomorphic curves with shift-invariant hyperplane preimages”, Trans. Amer. Math. Soc., 366, 4267–4298, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Korhonen, N. Li, K. Tohge, “Difference analogue of Cartan’s second main theorem for slowly moving periodic targets”, Ann. Acad. Sci. Fenn. Math., 41, 1–27, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. Korhonen, “A Difference Picard theorem for meromorphic functions of several variables”, Comput Method and Function Theory, 12(1), 343–361, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Ru, Nevanlinna theory and its relation to diophantime approximation (Word Scientific, Singapore, 2001).

    Book  Google Scholar 

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Authors and Affiliations

  1. Shandong University, Jinan, China

    N. V. Thin

  2. Thai Nguyen University of Education, Thai Nguyen city, Viet Nam

    N. V. Thin

Authors
  1. N. V. Thin
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Correspondence to N. V. Thin.

Additional information

Russian Text © The Author(s), 2019, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2019, No. 4, pp. 76–92.

The research was sponsored by China/Shandong University International Postdoctoral Exchange Program.

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Thin, N.V. A Difference Analogue of Cartan’s Second Main Theorem for Meromorphic Mappings. J. Contemp. Mathemat. Anal. 54, 240–252 (2019). https://doi.org/10.3103/S106836231904006X

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  • DOI: https://doi.org/10.3103/S106836231904006X

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