Proper holomorphic self-mappings of the minimal ball

Nabil Ourimi. "Proper holomorphic self-mappings of the minimal ball." Annales Polonici Mathematici 79.2 (2002): 97-107. <http://eudml.org/doc/280338>.

@article{NabilOurimi2002,
abstract = {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 $x∈ f^\{-1\}(b)$.},
author = {Nabil Ourimi},
journal = {Annales Polonici Mathematici},
keywords = {correspondences; branch locus; scaling; factorization; minimal ball; proper holomorphic self-mapping},
language = {eng},
number = {2},
pages = {97-107},
title = {Proper holomorphic self-mappings of the minimal ball},
url = {http://eudml.org/doc/280338},
volume = {79},
year = {2002},
}

TY - JOUR
AU - Nabil Ourimi
TI - Proper holomorphic self-mappings of the minimal ball
JO - Annales Polonici Mathematici
PY - 2002
VL - 79
IS - 2
SP - 97
EP - 107
AB - 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 $x∈ f^{-1}(b)$.
LA - eng
KW - correspondences; branch locus; scaling; factorization; minimal ball; proper holomorphic self-mapping
UR - http://eudml.org/doc/280338
ER -