Multitype et applications holomorphes propres. (Multitype and proper holomorphic mappings) (Q803340)

This paper gives, in a special case, the behavior of the multitype of a boundary point, under a proper holomorphic mapping near this point. More precisely: Let \(\Omega = \{z\in {\mathbb{C}}^ n;\;2 Re z_ 1+\sum^{n}_{i=2}| z_ i|^{2p_ i}<0\}\) and \(\Omega_ 0 = \{z\in {\mathbb{C}}^ n;\;2 Re z_ 1+\sum^{n}_{i=2}| z_ i|^{2q_ i}<0\}\) be two model domains in \({\mathbb{C}}^ n(p_ i,q_ i\in {\mathbb{N}}^*)\). Then the following result is proved: There exist neighborhoods U,V of 0 in \({\mathbb{C}}^ n\) and a proper holomorphic mapping u: \(\Omega\cap U\to \Omega_ 0\cap V\), \(C^{\infty}\) up to the boundary, if and only if there exist \(k_ 2,...,k_ n\) in \({\mathbb{N}}^*\) such that \(\{p_ 2,...,p_ n\}=\{k_ 2q_ 2,...,k_ nq_ n\}\).