New examples of effective formulas for holomorphically contractible functions

Marek Jarnicki; Peter Pflug

Studia Mathematica (1999)

  • Volume: 135, Issue: 3, page 219-230
  • ISSN: 0039-3223

Abstract

top
Let G n and B m be domains and let Φ:G → B be a surjective holomorphic mapping. We characterize some cases in which invariant functions and pseudometrics on G can be effectively expressed in terms of the corresponding functions and pseudometrics on B.

How to cite

top

Jarnicki, Marek, and Pflug, Peter. "New examples of effective formulas for holomorphically contractible functions." Studia Mathematica 135.3 (1999): 219-230. <http://eudml.org/doc/216652>.

@article{Jarnicki1999,
abstract = {Let $G ⊂ ℂ^n$ and $B ⊂ ℂ^m$ be domains and let Φ:G → B be a surjective holomorphic mapping. We characterize some cases in which invariant functions and pseudometrics on G can be effectively expressed in terms of the corresponding functions and pseudometrics on B.},
author = {Jarnicki, Marek, Pflug, Peter},
journal = {Studia Mathematica},
keywords = {holomorphically contractible function; invariant function; invariant pseudometric; Liouville property},
language = {eng},
number = {3},
pages = {219-230},
title = {New examples of effective formulas for holomorphically contractible functions},
url = {http://eudml.org/doc/216652},
volume = {135},
year = {1999},
}

TY - JOUR
AU - Jarnicki, Marek
AU - Pflug, Peter
TI - New examples of effective formulas for holomorphically contractible functions
JO - Studia Mathematica
PY - 1999
VL - 135
IS - 3
SP - 219
EP - 230
AB - Let $G ⊂ ℂ^n$ and $B ⊂ ℂ^m$ be domains and let Φ:G → B be a surjective holomorphic mapping. We characterize some cases in which invariant functions and pseudometrics on G can be effectively expressed in terms of the corresponding functions and pseudometrics on B.
LA - eng
KW - holomorphically contractible function; invariant function; invariant pseudometric; Liouville property
UR - http://eudml.org/doc/216652
ER -

References

top
  1. [Chi] E. M. Chirka, Complex Analytic Sets, Kluwer, 1989. Zbl0683.32002
  2. [Cyg] E. Cygan, Factorization of polynomials, Bull. Polish Acad. Sci. Math. 40 (1992), 45-52. Zbl0760.32004
  3. [Edi-Zwo 1] A. Edigarian and W. Zwonek, Invariance of the pluricomplex Green function under proper mappings with applications, Complex Variables 35 (1998), 367-380. 
  4. [Edi-Zwo 2] A. Edigarian and W. Zwonek, Proper holomorphic mappings in some class of unbounded domains, Kodai Math. J., to appear. 
  5. [For-Nar] J. E. Fornæss and R. Narasimhan, The Levi problem on complex spaces with singularities, Math. Ann. 248 (1980), 47-72. Zbl0411.32011
  6. [Jar-Pfl] M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, de Gruyter Exp. Math. 9, Walter de Gruyter, 1993. 
  7. [Lár-Sig] F. Lárusson and R. Sigurdsson, Plurisubharmonic functions and analytic discs on manifolds, preprint. Zbl0901.31004
  8. [Lel] P. Lelong, Fonction de Green pluricomplexe et lemmes de Schwarz dans les espaces de Banach, J. Math. Pures Appl. 68 (1989), 319-347. Zbl0633.32019
  9. [Pfl-Zwo] P. Pflug and W. Zwonek, Effective formulas for invariant functions-case of elementary Reinhardt domains, Ann. Polon. Math. 69 (1998), 175-196. Zbl0926.32015

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.