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

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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.

How to cite

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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

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  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

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