Proper holomorphic self-mappings of the minimal ball

Nabil Ourimi

Nabil Ourimi

Annales Polonici Mathematici, Tome 79 (2002), p. 97-107 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $f_{*} (π ₁ (D ∖ f^{- 1} (f (V_{f})), x))$ is a normal subgroup of $π ₁ (Ω ∖ f (V_{f}), b)$ for some $b \in Ω ∖ f (V_{f})$ and $x \in f^{- 1} (b)$ .

Publié le : 2002-01-01

Zbl 1020.32013

EUDML-ID : urn:eudml:doc:280338

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     year = {2002},
     pages = {97-107},
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Nabil Ourimi. Proper holomorphic self-mappings of the minimal ball. Annales Polonici Mathematici, Tome 79 (2002) pp. 97-107. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap79-2-1/