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

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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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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Keywords

  • Nevanlinna
  • Second main theorem
  • Meromorphic mapping
  • Moving hyperplane

Mathematics Subject Classification

  • Primary 32H30
  • 32A22
  • Secondary 30D35