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On the hyperconvexity of Reinhards domains. (English) Zbl 1143.32001
Imayoshi, Yoichi (ed.) et al., Complex analysis and applications. Proceedings of the 15th international conference on finite or infinite dimensional complex analysis and applications, Osaka, Japan, July 30–August 3, 2007. Osaka: Osaka Municipal Universities Press (ISBN 978-4-901409-37-7/hbk). OCAMI Studies 2, 261-265 (2007).
Let $$D$$ be a bounded domain in $$\mathbb C^n.$$ A weak Stein neighborhood basis of $$D$$ is a family of pseudoconvex domains $$\{\Omega_k\}_{k \geq 1}, k \in \mathbb{N}$$ such that $${\overline D} \subset \Omega_k$$ and $$D$$ is the interior of $$\bigcap \Omega_k.$$
The main result of this paper is the following Theorem 2. A bounded Reinhards domain $$D$$ in $$\mathbb C^n$$ having a weak Stein neighborhood basis is hyperconvex.
For the entire collection see [Zbl 1132.30002].
##### MSC:
 32A07 Special domains in $${\mathbb C}^n$$ (Reinhardt, Hartogs, circular, tube) (MSC2010) 32T05 Domains of holomorphy