Quasi-homogénéité des applications holomorphes propres d’un domaine quasi-disqué sur un domaine disqué

Moha Boutat[1]

  • [1] Université d’Angers, UMR 6093 LAREMA, 2 bd Lavoisier 49045 Angers cedex 01

Annales de la faculté des sciences de Toulouse Mathématiques (2011)

  • Volume: 20, Issue: 4, page 759-765
  • ISSN: 0240-2963

Abstract

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A result of F. Berteloot and G.Patrizio [1] states that if f is a proper holomorphic map between two bounded complete circular domains Ω 1 and Ω 2 in C n + 1 ( n ≥ 1 ) , such that f - 1 { 0 } = { 0 } and such that the principal part f p of the Taylor expansions of f at the origin is nondegenerated i.e f p - 1 { 0 } = { 0 } , then f ≡ f p . Here we propose to generalize their result in the case where Ω 1 is a complete quasi-circular domain and Ω 2 is a complete circular domain. Moreover this proof does not use the tools of projective dynamics of J. E. Fornaess and N. Sibony [3].

How to cite

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Boutat, Moha. "Quasi-homogénéité des applications holomorphes propres d’un domaine quasi-disqué sur un domaine disqué." Annales de la faculté des sciences de Toulouse Mathématiques 20.4 (2011): 759-765. <http://eudml.org/doc/219677>.

@article{Boutat2011,
abstract = {Nous proposons une généralisation d’un résultat de F. Berteloot et G. Patrizio [1], aux cas des applications holomorphes propres entre domaines quasi-disqués et non nécessairement bornés.},
affiliation = {Université d’Angers, UMR 6093 LAREMA, 2 bd Lavoisier 49045 Angers cedex 01},
author = {Boutat, Moha},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {proper holomorphic mapping; circular domain; quasi-circular domain; Taylor expansion; quasi-homogeneous map},
language = {fre},
month = {7},
number = {4},
pages = {759-765},
publisher = {Université Paul Sabatier, Toulouse},
title = {Quasi-homogénéité des applications holomorphes propres d’un domaine quasi-disqué sur un domaine disqué},
url = {http://eudml.org/doc/219677},
volume = {20},
year = {2011},
}

TY - JOUR
AU - Boutat, Moha
TI - Quasi-homogénéité des applications holomorphes propres d’un domaine quasi-disqué sur un domaine disqué
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/7//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - 4
SP - 759
EP - 765
AB - Nous proposons une généralisation d’un résultat de F. Berteloot et G. Patrizio [1], aux cas des applications holomorphes propres entre domaines quasi-disqués et non nécessairement bornés.
LA - fre
KW - proper holomorphic mapping; circular domain; quasi-circular domain; Taylor expansion; quasi-homogeneous map
UR - http://eudml.org/doc/219677
ER -

References

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  1. Berteloot (F.) and Patrizio (G.).— A Cartan theorem for proper holomorphic mappings of complete circular domains, Advances in math 153, p. 342-352 (2000). Zbl0962.32020MR1770933
  2. Boutat (M.).— Applications holomorphes propres d’un domaine quasi-disqué sur un domaine disqué, Bulletin des Sciences Mathématiques Volume 133, Issue 4, May p. 335-347 (2009). Zbl1176.32006MR2532688
  3. Fornaess (J. E.) and Sibony (N.).— Complex dynamics in higher dimensions, in “Complex Pluripotential theory,”, NATO Adv. Sci. Inst. Ser. C. Math. Phys. Sci., Vol. 439, pp. 131-186, Kluwer Academic, Dordrecht (1994). Zbl0811.32019MR1332961
  4. Barth (T.).— The Kobayashi indicatrix at the center of a circular domain, Proc. Amer. Math. Soc. 88, p. 527-530 (1983). Zbl0494.32008MR699426
  5. Chirka (E.M.), Delbeault (P.), Khenkin (G.M.), Vitushkin (A.G.).— Introduction to complex analysis, Springer-Verlag (1997). Zbl0947.32001MR1734390

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