Envelopes of holomorphy of Hartogs and circular domains
type: Item
instance of: scholarly article
title: Envelopes of holomorphy of Hartogs and circular domains
zbMATH Open document ID: 0685.32008
author: Enrico Casadio Tarabusi
author: Stefano Trapani
published in: Pacific Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: The classical problem of the univalence and description of the envelope of holomorphy of a domain in \({\mathbb{C}}^ n\) is investigated: the classes of Hartogs and circular domains are taken into consideration. In the Hartogs case preceding results are improved and completed. For instance, the problem is solved for domains such that the fibers of the projection onto the hyperplane of symmetry are connected: they include complete Hartogs domains as particular cases. These results are transferred to the circular case using the fact that a circular domain which does not intersect some hyperplane through the origin is biholomorphic to a Hartogs domain; the general case is then inferred from this and other considerations. An alternative interpretation of these results is given in terms of fiber bundles over the projective space \({\mathfrak P}^{n-1}({\mathbb{C}}).\) Suitable examples show the noneliminability of the assumptions of `connected sections' from any of our main statements.
reviewed by: Enrico Casadio Tarabusi
Mathematics Subject Classification ID: 32D10
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 4122318
zbMATH Keywords: plurisubharmonic function
zbMATH Keywords: envelope of holomorphy
zbMATH Keywords: circular domains
zbMATH Keywords: Hartogs domains
MaRDI profile type: Publication
full work available at URL: pjm.1991.149.231
OpenAlex ID: W2031653583
DOI: 10.2140/PJM.1991.149.231
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description: scientific article; zbMATH DE number 4122318