We construct an unbounded strictly pseudoconvex Kobayashi hyperbolic and complete domain in \({\mathbb {C}}^2\), which also possesses complete Bergman metric, but has no nonconstant bounded holomorphic functions.

中文翻译：

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Kobayashi和Bergman的完整域，无界表示

我们在\（{\ mathbb {C}} ^ 2 \）中构造一个无界的严格伪凸Kobayashi双曲且完整域，该域也具有完整的Bergman度量，但没有非恒定有界全纯函数。