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Approximation and Subextension of Negative Plurisubharmonic Functions
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
2008 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we study approximation of negative plurisubharmonic functions by functions defined on strictly larger domains. We show that, under certain conditions, every function u that is defined on a bounded hyperconvex domain Ω in Cn and has essentially boundary values zero and bounded Monge-Ampère mass, can be approximated by an increasing sequence of functions {uj} that are defined on strictly larger domains, has boundary values zero and bounded Monge-Ampère mass. We also generalize this and show that, under the same conditions, the approximation property is true if the function u has essentially boundary values G, where G is a plurisubharmonic functions with certain properties. To show these approximation theorems we use subextension. We show that if Ω_1 and Ω_2 are hyperconvex domains in Cn and if u is a plurisubharmonic function on Ω_1 with given boundary values and with bounded Monge-Ampère mass, then we can find a plurisubharmonic function û defined on Ω_2, with given boundary values, such that û <= u on Ω and with control over the Monge-Ampère mass of û.

Place, publisher, year, edition, pages
Umeå: Matematik och matematisk statistik , 2008. , 9 p.
Keyword [en]
Complex Monge-Ampère operator, Approximation, Plurisubharmonic function, Subextension
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-1799ISBN: 978-91-7264-622-3 (print)OAI: oai:DiVA.org:umu-1799DiVA: diva2:142007
Presentation
2008-08-25, N430, Naturvetarhuset, Umeå, 13:15
Opponent
Supervisors
Available from: 2008-09-02 Created: 2008-09-02Bibliographically approved
List of papers
1. Subextension and approximation of negative plurisubharmonic functions
Open this publication in new window or tab >>Subextension and approximation of negative plurisubharmonic functions
2008 (English)In: The Michigan mathematical journal, ISSN 0026-2285, Vol. 56, 593-601 p.Article in journal (Refereed) Published
Identifiers
urn:nbn:se:umu:diva-3344 (URN)
Available from: 2008-09-02 Created: 2008-09-02 Last updated: 2009-06-23Bibliographically approved
2. Subextension of plurisubharmonic functions without increasing the total Monge-Ampère mass
Open this publication in new window or tab >>Subextension of plurisubharmonic functions without increasing the total Monge-Ampère mass
Article in journal (Refereed) Submitted
Identifiers
urn:nbn:se:umu:diva-3345 (URN)
Available from: 2008-09-02 Created: 2008-09-02Bibliographically approved
3. Approximation of negative plurisubharmonic functions with given boundary values
Open this publication in new window or tab >>Approximation of negative plurisubharmonic functions with given boundary values
Article in journal (Refereed) Submitted
Identifiers
urn:nbn:se:umu:diva-3346 (URN)
Available from: 2008-09-02 Created: 2008-09-02Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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Output format
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