Proper holomorphic self-mappings of the minimal ball

• Autorzy: Nabil Ourimi
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to prove that proper holomorphic self-mappings of the minimal ball are biholomorphic. The proof uses the scaling technique applied at a singular point and relies on the fact that a proper holomorphic mapping f: D → Ω with branch locus $V_f$ is factored by automorphisms if and only if $f_{*}(π₁(D ∖ f^{-1} (f(V_f)),x))$ is a normal subgroup of $π₁(Ω ∖ f(V_f),b)$ for some $b ∈ Ω ∖ f(V_f)$ and $x∈ f^{-1}(b)$.

Kategorie tematyczne

• 32H35: Proper mappings, finiteness theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2002
• Tom: 79
• Numer: 2
• Strony: 97-107

Daty

wydano

2002

Twórcy

autor

Nabil Ourimi

• ICTP, Math. Section, Strada Costiera, II, 34014 Trieste, Italy
• Faculté des sciences de Bizerte, 7021 Jarzouna, Tunisie

Identyfikatory

DOI

10.4064/ap79-2-1