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Fatou-Bieberbach domains with \(C^ \infty\)-smooth boundary. (English) Zbl 0883.32020

An open domain \(\Omega\) in \(\mathbb{C}^n\) is called a Fatou-Bieberbach domain if \(\Omega\) is a proper subdomain in \(\mathbb{C}^n\) and biholomorphically equivalent to \(\mathbb{C}^n\).
The author proves that there exists a Fatou-Bieberbach domain in \(\mathbb{C}^2\) with \(C^\infty\)-smooth boundary.
Reviewer: Z.Ye (DeKalb)

MSC:

32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
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