Embeddings and proper holomorphic maps of strictly pseudoconvex domains into polydiscs and balls
type: Item
instance of: scholarly article
title: Embeddings and proper holomorphic maps of strictly pseudoconvex domains into polydiscs and balls
zbMATH Open document ID: 0584.32048
DOI: 10.1007/BF01215140
author: Erik Løw
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173635
review text: This paper contains some interesting results on the topics stated in the title. In an earlier paper the author had shown that the unit ball \(B_ n\) in \({\mathbb{C}}^ n\) can be embedded as a closed complex submanifold of a polydisc in some higher dimension. In the first part of the present paper he generalizes this result from the ball to an arbitrary strictly pseudoconvex domain with \(C^ 2\) boundary. This result is based on the Hakim-Sibony-Løw construction of inner functions on the ball, and its extension to strictly pseudoconvex domains [the author, Math. Zeitschr. 185, 191-210 (1984; Zbl 0508.32005)]. In the second part the author proves that every strictly pseudoconvex domain with \(C^ 2\) boundary also admits a proper holomorphic embedding into some higher dimensional ball, which extends continuously to the boundary. Again, the construction is quite explicit, based on modifications of the techniques used for the embedding into polydiscs. This latter result was also obtained independently by \textit{F. Forstneric} [Preprint Ser. Dept. Math., Univ. Ljubljana, 23, no. 153 (1985)] and Hakim and Sibony (unpublished); these authors also give examples of proper holomorphic maps \(B_ n\to B_ N\), \(N>n\), which do not extend continuously to the boundary.
reviewed by: R. Michael Range
Mathematics Subject Classification ID: 32H35
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32E35
Mathematics Subject Classification ID: 14E25
Mathematics Subject Classification ID: 30D50
Mathematics Subject Classification ID: 32H99
zbMATH DE Number: 3935476
zbMATH Keywords: proper holomorphic maps of strictly pseudoconvex domains into polydiscs and balls
zbMATH Keywords: continuous extension to the boundary
zbMATH Keywords: Hakim-Sibony-Løw construction of inner functions
zbMATH Keywords: proper holomorphic embedding
MaRDI profile type: Publication
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OpenAlex ID: W2009156705
description: scientific article; zbMATH DE number 3935476