## 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

### Keywords:

Fatou-Bieberbach domain
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