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Second main theorem with weighted counting functions and uniqueness theorem

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In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of $\pn$ where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.

Abstract

In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of $\pn$ where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.

참고문헌 (11)

  1. Z. Chen, "Uniqueness problem with truncated multiplicities of mero"morphic mappings for moving targets", Acta Math. Sci. Ser. B(Engl. Ed. ), 27(3), pp.625~634 (2007)[DOI]
  2. Junjiro Noguchi, "Nevanlinna Theory in Several Complex Variables and Diophantine Approximation", Grundlehren der mathematischen Wissenschaften (2014), Springer Japan[DOI]
  3. H. H. Pham, "Unicity theorems with truncated multiplicities of meromorphic mappings in several complex variables sharing small identical sets for moving targets", Internat. J. Math, 21(9), pp.1095~1120 (2010)[DOI]
  4. S. D. Quang, "Second main theorems with weighted counting functions and algebraic dependence of meromorphic mappings", Proc. Amer. Math. Soc, 144(10), pp.4329~4340 (2016)[DOI]
  5. S. D. Quang, "Generalization of uniqueness theorem for meromorphic mappings sharing hyperplanes", Internat. J. Math, 30(1), pp.1950011~ (2019)
  6. Si Duc Quang, "Second main theorem for holomorphic maps from complex disks with moving hyperplanes", Complex Variables and Elliptic Equations, 68(1), pp.150~166 (2021), Informa UK Limited[DOI]
  7. M. Ru, "Nevanlinna Theory and Its Relation to Diophantine Approximation" (2001), World Scientific Publishing Co., Inc
  8. M. Ru, "A uniqueness theorem with moving targets without counting multiplicity", Proc. Amer. Math. Soc, 129(9), pp.2701~2707 (2001)[DOI]
  9. M. Ru, "The second main theorem in the hyperbolic case", Math. Ann, 377(1-2), pp.759~795 (2020)[DOI]
  10. M. Ru, "Uniqueness results for holomorphic mappings on the disc", Acta Math. Vietnam, 45(1), pp.71~81 (2020)[DOI]
  11. L. Yang, "Uniqueness theorem for holomorphic curves on the disc", Publ. Math. Debrecen, 98(3-4), pp.299~312 (2021)

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