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Second main theorems for meromorphic mappings intersecting moving hyperplanes with truncated counting functions and unicity problem

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Abstract

In this article, we establish some new second main theorems for meromorphic mappings of \({\mathbf {C}}^m\) into \({\mathbf {P}}^n({\mathbf {C}})\) and moving hyperplanes with truncated counting functions. Our results are improvements of the previous second main theorems for moving hyperplanes with truncated (to level n) counting functions. As an application, a unicity theorem for meromorphic mappings sharing moving hyperplanes is given.

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References

  1. Fujimoto, H.: Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into \({\mathbf{P}}^{N_1}({\mathbf{C}})\times \cdots \times {\mathbf{P}}^{N_k}({\mathbf{C}})\). Jpn. J. Math. 11, 233–264 (1985)

    MathSciNet  Google Scholar 

  2. Fujimoto, H.: Uniqueness problem with truncated multiplicities in value distribution theory. Nagoya Math. J. 152, 131–152 (1998)

    MathSciNet  MATH  Google Scholar 

  3. Noguchi, J., Ochiai, T.: Introduction to Geometric Function Theory in Several Complex Variables. In: Translations of Mathematical Monographs, American Mathematical Society, vol. 80. Providence, Rhode Island (1990)

  4. Ru, M.: A uniqueness theorem with moving targets without counting multiplicity. Proc. Am. Math. Soc. 129, 2701–2707 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ru, M., Wang, J.T.-Y.: Truncated second main theorem with moving targets. Trans. Am. Math. Soc. 356, 557–571 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Shiffman, B.: Introduction to the Carlson-Griffiths equidistribution theory. In: Lecture Notes in Math. 981, 44–89 (1983)

  7. Thai, D.D., Quang, S.D.: Uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables for moving targets. Int. J. Math. 16, 903–939 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Thai, D.D., Quang, S.D.: Second main theorem with truncated counting function in several complex variables for moving targets. Forum Mathematicum 20, 145–179 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Yamanoi, K.: The second main theorem for small functions and related problems. Acta Math. 192, 225–294 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This work was done during a stay of the author at the Vietnam Institute for Advanced Study in Mathematics. He would like to thank the institute for their support. This research was supported in part by a NAFOSTED Grant of Vietnam (Grant No. 101.04-2015.03).

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Correspondence to Si Duc Quang.

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Communicated by Bernd Siebert.

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Quang, S.D. Second main theorems for meromorphic mappings intersecting moving hyperplanes with truncated counting functions and unicity problem. Abh. Math. Semin. Univ. Hambg. 86, 1–18 (2016). https://doi.org/10.1007/s12188-015-0114-1

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  • DOI: https://doi.org/10.1007/s12188-015-0114-1

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