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Singular Directions of Brody Curves

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Abstract

In this paper, we give a version of “angular domain” type for the results of Da Costa and Duval (Math Ann 355(4):1593–1600, 2013) for Brody curves into a complex projective algebraic variety in \(P^N({\mathbb {C}})\) intersecting hypersurfaces. Based on this version, we also establish the existence of singular directions of Brody curves into algebraic varieties.

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References

  1. Da Costa, B.F.P.: pp. 1–42. www.theses.fr/2012PA112106.pdf (2012)

  2. Da Costa, B.F.P., Duval, J.: Sur les courbes de Brody dans \(P^n({\mathbb{C}})\). Math. Ann. 355(4), 1593–1600 (2013)

    Article  MathSciNet  Google Scholar 

  3. Eremenko, A.: Julia directions for holomorphic curves. Preprint in A. Eremenkos home page

  4. Grishin, A.: Sets of regular growth of entire functions. I (Russian) Teor. Funkts i Funktsional. Anal. I Prilozhen. 40, 36–47 (1983)

    MathSciNet  MATH  Google Scholar 

  5. Hormander, L.: Analysis of Linear Partial Differential Operators I, Distribution Theory and Fourier Analysis. Springer, Berlin (1983)

    MATH  Google Scholar 

  6. Julia, G.: Sur quelques proprietes nouvelles des functions entieres ou meromorphes (premier mémoire). Ann. Sci. Ec. Norm. Sup. 36, 93–125 (1916)

    Article  Google Scholar 

  7. Julia, G.: Sur quelques proprietes nouvelles des functions entieres ou meromorphes (deuxime mémoire). Ann. Sci. Ec. Norm. Sup. 37, 165–218 (1920)

    Article  Google Scholar 

  8. Milloux, H.: Le théorme de Picard, suites de functions holomorphes, functions holomorphes et functions entieres. J. Math. Pures Appl. 3, 345–401 (1924)

    Google Scholar 

  9. Matsuo, S., Tsukamoto, M.: Brody curves and mean dimension. J. Am. Math. Soc. 28, 159–182 (2015)

    Article  MathSciNet  Google Scholar 

  10. Tsukamoto, M.: Mean dimension of the dynamical system of Brody curves. Invent. Math. 211, 935–968 (2018)

    Article  MathSciNet  Google Scholar 

  11. Valiron, G.: Directions de Borel des Fonctions Meromorphes, Memor Sci Math Fasc 89. GauthierVillars et Cie, Paris (1938)

    Google Scholar 

  12. Zheng, J.H.: Value distribution of holomorphic curves on an angular domain. Mich. Math. J. 64, 849–879 (2015)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We would like to express our gratitude to the referee. His/her valuable comments made on the first version of this paper led to significant improvements in the paper. This work was done during a stay of the first author at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank VIASM for the partial support, and the staff of VIASM for their hospitality.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, 136 XuanThuy str., Hanoi, Vietnam

    Do Duc Thai

  2. Basic Sciences Faculty, Foreign Trade University, 91 ChuaLang Str., Hanoi, Vietnam

    Pham Ngoc Mai

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  1. Do Duc Thai
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  2. Pham Ngoc Mai
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Correspondence to Do Duc Thai.

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The research of the authors is supported by an NAFOSTED Grant of Vietnam (Grant No. 101.04-2017.317).

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Thai, D.D., Mai, P.N. Singular Directions of Brody Curves. J Geom Anal 31, 1721–1731 (2021). https://doi.org/10.1007/s12220-019-00322-z

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  • DOI: https://doi.org/10.1007/s12220-019-00322-z

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