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Plurisubharmonic extension in non-degenerate analytic polyhedra
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.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
Responsible organisation
2007 (English)In: Universitatis Iagellonicae Acta Mathematica, ISSN 0860-0120, no 45, 139-145 p.Article in journal (Refereed) Published
Abstract [en]

Let $mathcal{P}$ be a connected, non-degenerate analytic polyhedron in $mathbb{C}^n$, $ngeq 2$. In this note we characterize those continuous functions which can be extended to a plurisubharmonic function in $mathcal{P}$.

Place, publisher, year, edition, pages
2007. no 45, 139-145 p.
Keyword [en]
analytic discs, analytic polyhedra, Dirichlet problem, Jensen measures, plurisubharmonic functions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-4385Local ID: 5294OAI: oai:DiVA.org:miun-4385DiVA: diva2:29417
Available from: 2008-09-30 Created: 2009-09-15 Last updated: 2011-09-05Bibliographically approved
In thesis
1. Holomorphic embeddings and applications
Open this publication in new window or tab >>Holomorphic embeddings and applications
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In the first part of this thesis we consider the question of the number of equivalence

classes of holomorphic embeddings of Ck into Cn. We show the existence of holomorphic

families of proper holomorphic embeddings of Ck into Cn (0 < k < n−1),

such that members of the family are pairwise nonequivalent in a suitable sense. As

an application we use these embeddings to deduce results in the theory of holomorphic

transformation groups.

In the second part of the thesis the question of plurisubharmonic extension is connected

to analytic discs, i.e. nonconstant holomorphic maps of the unit disc in C

into Cn. We derive results on plurisubharmonic extension for analytic polyhedra.

Place, publisher, year, edition, pages
Sundsvall: Mittuniversitetet, 2009
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 67
Keyword
Anders´en-Lempert-theory, holomorphic embeddings, Eisenman hyperbolicity, holomorphic group actions, plurisubharmonic extension, analytic polyhedron
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-9634 (URN)978-91-86073-27-5 (ISBN)
Public defence
2009-02-06, L 111, Mittuniversitetet, Campus Sundsvall, Sundsvall, 10:15 (English)
Supervisors
Available from: 2009-09-15 Created: 2009-09-15 Last updated: 2014-10-01Bibliographically approved

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Citation style
  • apa
  • harvard1
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  • en-US
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  • Other locale
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