JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Proper holomorphic self-mappings of the minimal ball

### Tom 79 / 2002

Annales Polonici Mathematici 79 (2002), 97-107 MSC: Primary 32H35. DOI: 10.4064/ap79-2-1

#### Streszczenie

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 $f: D\rightarrow {\mit \Omega }$ with branch locus $V_f$ is factored by automorphisms if and only if $f_{*}(\pi _1(D\setminus f^{-1} (f(V_f)), x))$ is a normal subgroup of $\pi _1({\mit \Omega } \setminus f(V_f), b)$ for some $b\in {\mit \Omega } \setminus f(V_f)$ and $x\in f^{-1}(b)$.

#### Autorzy

• Nabil OurimiICTP
Math. Section