Skip to main content
SpringerLink
Log in

On two conjectures for convex biholomorphic mappings in ℂn

  • Published:
Journal d’Analyse Mathematique Aims and scope

Abstract

In this paper, we consider the problem of distortion theorems for mappings which map the unit ball biholomorphically onto convex domains in ℂn. In particular, we discuss two distortion conjectures for such mappings.

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. H. Chen and P. M. Gauthier,Bloch constants in several variables, Trans. Amer. Math. Soc.353 (2000), 1371–1386.

    Article  MathSciNet  Google Scholar 

  2. I. Graham and G. Kohr,Univalent mappings associated with the Roper-Suffridge extension operator, J. Analyse Math.81 (2000), 331–342.

    MATH  MathSciNet  Google Scholar 

  3. P. Liczberski,Applications of a decomposition of holomorphic mappings in ℂ n with respect to a cyclic group, J. Math. Anal. Appl.281 (2003), 282–292.

    MathSciNet  Google Scholar 

  4. P. Liczberski and V. V. Starkov,Distortion theorems for biholomorphic convex mappings in ℂ n, J. Math. Anal. Appl.274 (2002), 495–504.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. A. Pfaltzgraff and T. J. Suffridge,Norm order and geometric properties of holomorphic mappings in ℂ n, J. Analyse Math.82 (2000), 285–313.

    MATH  MathSciNet  Google Scholar 

  6. E. A. Poletsky,Holomorphic quasiregular mappings, Proc. Amer. Math. Soc.92 (1985), 325–341.

    MathSciNet  Google Scholar 

  7. K. A. Roper and T. J. Suffridge,Convex mappings on the unit ball of ℂ n, J. Analyse Math.65 (1995), 333–347.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Technical University of Łódź, Ul. Zwirki 36, 90-924, Łódź, Poland

    Piotr Liczberski & Victor V. Starkov

  2. Faculty of Mathematics, Petrozavodsk State University, Pr. Lenina, 185640, Petrozavodsk, Russia

    Victor V. Starkov

Authors
  1. Piotr Liczberski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Victor V. Starkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Piotr Liczberski.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liczberski, P., Starkov, V.V. On two conjectures for convex biholomorphic mappings in ℂn . J. Anal. Math. 94, 377–383 (2004). https://doi.org/10.1007/BF02789055

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02789055

Keywords

Search

Navigation