Hyperbolicity of circular domains
A domain \(D\subset {\mathbb{C}}^ n\) is called strictly starlike circular if D contains the origin and \((i)\quad \lambda D\subset D\) for all \(\lambda\in {\mathbb{C}}\) with \(| \lambda | \leq 1\), (ii) closure \(\bar D\subset \lambda D\) for any real \(\lambda >1\). It is proved that if every \({\mathbb{C}}\)-linear map from \({\mathbb{C}}\) to D is zero, then D is bounded and consequently is hyperbolic in Kobayashi sense. It is given an example of pseudoconvex circular domain in \({\mathbb{C}}^ 2\) which contains no entire holomorphic curve and is not hyperbolic.
scientific article; zbMATH DE number 3882735
scientific article