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

Abstract :

A result of F. Berteloot and G.Patrizio [1] states that if f is a proper holomorphic map between two bounded complete circular domains Ω1 and Ω2 in C n+1 (n≥1), such that f -1 {0}={0} and such that the principal part fp of the Taylor expansions of f at the origin is nondegenerated i.e fp -1 {0}={0}, then f≡fp . Here we propose to generalize their result in the case where Ω1 is a complete quasi-circular domain and Ω2 is a complete circular domain. Moreover this proof does not use the tools of projective dynamics of J. E. Fornaess and N. Sibony [3].

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https://hal.archives-ouvertes.fr/hal-01389255
Contributor : Okina Université d'Angers <>
Submitted on : Friday, October 28, 2016 - 11:12:40 AM
Last modification on : Monday, March 9, 2020 - 6:16:02 PM

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Moha Ou Ali Boutat. Quasi-homogénéité des applications holomorphes propres d’un domaine quasi-disqué sur un domaine disqué. Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc 2011, 20 (4), pp.759 - 765. ⟨10.5802/afst.1322⟩. ⟨hal-01389255⟩

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