A remark on semiglobal existence for \(\overline{\partial}\)
type: Item
instance of: scholarly article
title: A remark on semiglobal existence for \(\overline{\partial}\)
zbMATH Open document ID: 0896.32009
author: Alberto Scalari
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1997-11-19T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108428
review text: Let \(\Omega\) be a domain in \(\mathbb{C}^n\) with \(C^2\)-boundary. Then it is known that \(\Omega\) is pseudoconvex if (and only if) \(\Omega\) can be exhausted by a sequence of relatively compact pseudoconvex subdomains \(\Omega_i \Subset \Omega\). Hörmander gave a proof of this result with the so called \(\overline \partial\) technique (reference [6] in this paper). Here, the author provides a simpler proof of that result, by using the Hörmander technique. However, I have some trouble to follow his argument. Furthermore, the author lists 9 papers in the references; in fact actually, in the paper itself, only two were referred to.
reviewed by: Tan Vovan
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 1089768
zbMATH Keywords: semiglobal existence for \(\overline\partial\)
zbMATH Keywords: pseudoconvex domain
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1089768