Skip to main content
SpringerLink
Log in

Normal Holomorphic Mappings in Complex Space

  • Published:
Complex Analysis and Operator Theory Aims and scope Submit manuscript

Abstract

We study normal holomorphic mappings on complex spaces and complex manifolds. Applications are provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yosida, K.: On a class of meromorphic functions. Proc. Phys. Math. Soc. Jpn III. Ser. 16, 227–235 (1934)

    Google Scholar 

  2. Noshiro, K.: Contributions to the theory of meromorphic functions in the unit-circle. J. Fac. Sci. Hokkaido Univ. Ser. I 7, 149–159 (1939)

    Google Scholar 

  3. Lehto, O., Virtanen, K.I.: Boundary Behaviour and normal meromorphic functions. Acta Math. 97, 47–65 (1957)

    Article  MathSciNet  Google Scholar 

  4. Cima, J.A., Krantz, S.G.: The Lindelöf principle and normal functions of several complex variables. Duke Math. J. 50, 303–328 (1983)

    Article  MathSciNet  Google Scholar 

  5. Marty, F.: Recherches sur la répartition des valeurs d’une fonction méromorphe. Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. (3) 23, 183–261 (1931)

    MathSciNet  Google Scholar 

  6. Dovbush, P.V.: Zalcman’s lemma in \({\mathbb{C} }^n\). Complex Var. Elliptic Equ. 65(5), 796–800 (2020)

    Article  MathSciNet  Google Scholar 

  7. Fujimoto, H.: On families of meromorphic maps into the complex projective space. Nagoya Math. J. 54, 21–51 (1974)

    Article  MathSciNet  Google Scholar 

  8. Kiernan, P.: Hyperbolically imbedded spaces and the big Picard theorem. Math. Ann. 204, 203–209 (1973)

    Article  MathSciNet  Google Scholar 

  9. Green, M.L.: The hyperbolicity of the complement of \(2n + 1\) hyperplanes in general position in \(P_n\) and related results. Proc. Am. Math. Soc. 66, 109–113 (1977)

    Google Scholar 

  10. Green, M.L.: Holomorphic maps to complex tori. Am. J. Math. 100, 615–620 (1978)

    Article  MathSciNet  Google Scholar 

  11. Dovbush, P.V.: Normal functions of many complex variables. Vestnic Moskov. Univ. Ser. I Mat. Mekh. no. 1, pp. 38–42 (1981). [English transl. in Mosk. Univ. Math. Bull., 36 (1981), no. 1, 44-48], MR613124 (83i:32006)

  12. Dovbush, P.V.: Lindelöf theorem in \(\mathbb{C}^n\). Mosc. Univ. Math. Bull. 36(6), 41–44 (1981); translation from Vestn. Mosk. Univ., Ser. I, 1981, No. 6, 33-36 (1981), Zbl. 0489.32002

  13. Montel, P.: Sur les suites infinies de fonctions. Ann. Sci. Éc. Norm. Supér. (3) 24, 233–234 (1907)

    Article  MathSciNet  Google Scholar 

  14. Valiron, G.: Sur les théorèmes de M. M. Bloch, Landau, Montel et Schottky. C. R. Acad. Sci. Paris 183, 728–730 (1926)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Moldova State University, 5 Academy Street, MD-2028, Kishinev, Republic of Moldova

    Peter V. Dovbush & Steven G. Krantz

  2. Washington University in St. Louis, St. Louis, MO, 63130, USA

    Peter V. Dovbush & Steven G. Krantz

Authors
  1. Peter V. Dovbush
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steven G. Krantz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Steven G. Krantz.

Additional information

Communicated by Daniele Struppa.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of Topical Collection in Honor of Prof. John Ryan’s Retirement.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dovbush, P.V., Krantz, S.G. Normal Holomorphic Mappings in Complex Space. Complex Anal. Oper. Theory 18, 28 (2024). https://doi.org/10.1007/s11785-023-01457-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11785-023-01457-2

Keywords

Mathematics Subject Classification

Search

Navigation