Jarnicki, M.; Pflug, P. Bergman completeness of complete circular domains. (English) Zbl 0701.32002 Ann. Pol. Math. 50, No. 2, 219-222 (1989). A domain \(D\subset {\mathbb{C}}^ n\) is called complete circular if whenever \(z\in D\), \(\lambda\in {\mathbb{C}}\), \(| \lambda | \leq 1\) then \(\lambda\) \(z\in D\). Any such domain can be defined by \(D=\{z\in {\mathbb{C}}^ n|\) \(h(z)<1\}\) where h: \({\mathbb{C}}^ n\to [0,\infty)\) is its Minkowski functional and D is a domain of holomorphy iff h is plurisubharmonic. The main result of this paper is the following: Any bounded complete circular domain of holomorphy with continuous Minkowski functional is complete with respect to the Bergman metric. The proof is essentially based on a result of Ohsawa and Takegoshi on the extension of \(L^ 2\) holomorphic functions. Reviewer: M.Colţoiu Cited in 2 ReviewsCited in 8 Documents MSC: 32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010) 32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.) 32D05 Domains of holomorphy Keywords:Reinhardt domain; domain of holomorphy; complete circular domain; Bergman metric PDFBibTeX XMLCite \textit{M. Jarnicki} and \textit{P. Pflug}, Ann. Pol. Math. 50, No. 2, 219--222 (1989; Zbl 0701.32002) Full Text: DOI