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Non-equivalent embeddings into complex Euclidean spaces
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Responsible organisation
2006 (English)In: International Journal of Mathematics, ISSN 0129-167X, Vol. 17, no 9, 1033-1046 p.Article in journal (Refereed) Published
Abstract [en]

We study the number of equivalence classes of proper holomorphic embeddings of a Stein space X into ℂn. In this paper we prove that if the automorphism group of X is a Lie group and there exists a proper holomorphic embedding of X into ℂn, 0 < dim X < n, then for any k ≥ 0 there exist uncountably many non-equivalent proper holomorphic embeddings Φ: X × ℂk ℂn × ℂk. For k = 0 all embeddings will be proved to satisfy the additional property of ℂn\Φ(X) being (n - dim X)-Eisenman hyperbolic. As a corollary we conclude that there are uncountably many non-equivalent proper holomorphic embeddings of ℂk into ℂn whenever 0 < k < n.

Place, publisher, year, edition, pages
2006. Vol. 17, no 9, 1033-1046 p.
Keyword [en]
proper holomorphic embeddings, hyperbolicity, Eisenman, complex analysis
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-3420DOI: 10.1142/S0129167X06003795ISI: 000242603500002Scopus ID: 2-s2.0-33750928991Local ID: 3404OAI: oai:DiVA.org:miun-3420DiVA: diva2:28452
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2016-09-30Bibliographically approved

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Borell, StefanKutzschebauch, Frank
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CiteExportLink to record
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Citation style
  • apa
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