Advertisement

Vietnam Journal of Mathematics

, Volume 41, Issue 4, pp 383–398 | Cite as

Unicity of Meromorphic Mappings Sharing Few Moving Hyperplanes

  • Si Duc QuangEmail author
  • Do Phuong An
Article

Abstract

In this paper, the Second Main Theorem for moving targets given by Thai–Quang (Forum Math. 20:163–179, 2008) is generalized. As its applications, some unicity theorems for meromorphic mappings of C m into the complex projective space P n (C) sharing moving hyperplanes regardless of multiplicities are shown.

Keywords

Meromorphic mapping Unicity theorem Second main theorem Truncated multiplicity Moving hyperplane 

Mathematics Subject Classification (2010)

32H30 32A22 30D35 

Notes

Acknowledgements

The authors would like to thank Professor Do Duc Thai for many useful suggestions concerning this material. The research of the authors is supported by an NAFOSTED grant of Vietnam (Grant No. 101.01-2011.29).

References

  1. 1.
    Chen, Z., Li, Y., Yan, Q.: Uniqueness problem with truncated multiplicities of meromorphic mappings for moving targets. Acta Math. Sci. Ser. B Engl. Ed. 27, 625–634 (2007) CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Dethloff, G., Tan, T.V.: Uniqueness problem for meromorphic mappings with truncated multiplicities and moving targets. Nagoya J. Math. 181, 75–101 (2006) zbMATHMathSciNetGoogle Scholar
  3. 3.
    Ha, P.H., Quang, S.D., Thai, D.D.: Uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables sharing small identical sets for moving target. Int. J. Math. 21, 1095–1120 (2010) CrossRefzbMATHGoogle Scholar
  4. 4.
    Jin, L., Ru, M.: A unicity theorem for moving targets counting multiplicities. Tohoku Math. J. 57, 589–595 (2005) CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Noguchi, J., Ochiai, T.: Introduction to Geometric Function Theory in Several Complex Variables. Trans. Math. Monogr., vol. 80. Am. Math. Soc., Providence (1990) Google Scholar
  6. 6.
    Ru, M.: A uniqueness theorem with moving targets without counting multiplicity. Proc. Am. Math. Soc. 129, 2701–2707 (2001) CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Ru, M., Wang, J.T.-Y.: Truncated second main theorem with moving targets. Trans. Am. Math. Soc. 356, 557–571 (2004) CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Thai, D.D., Quang, S.D.: Uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables for moving target. Int. J. Math. 16, 903–939 (2005) CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Thai, D.D., Quang, S.D.: Second main theorem with truncated counting function in several complex variables for moving targets. Forum Math. 20, 163–179 (2008) zbMATHMathSciNetGoogle Scholar
  10. 10.
    Thoan, P.D., Duc, P.V., Quang, S.D.: Algebraic dependence and unicity theorem with a truncation level to 1 of meromorphic mappings sharing moving targets. Bull. Math. Soc. Sci. Math. Roumanie 56(104), 2 (2013) Google Scholar
  11. 11.
    Tu, Z.-H.: Uniqueness problem of meromorphic mappings in several complex variables for moving targets. Tohoku Math. J. 54, 567–579 (2002) CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2013

Authors and Affiliations

  1. 1.Department of MathematicsHanoi National University of EducationCau GiayVietnam

Personalised recommendations