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Boundary values of plurisubharmonic functions and related topics
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of three papers concerning problems related to plurisubharmonic functions on bounded hyperconvex domains, in particular boundary values of such functions. The papers summarized in this thesis are:* Paper I Urban Cegrell and Berit Kemppe, Monge-Ampère boundary measures, Ann. Polon. Math. 96 (2009), 175-196.* Paper II Berit Kemppe, An ordering of measures induced by plurisubharmonic functions, manuscript (2009).* Paper III Berit Kemppe, On boundary values of plurisubharmonic functions, manuscript (2009).In the first paper we study a procedure for sweeping out Monge-Ampère measures to the boundary of the domain. The boundary measures thus obtained generalize measures studied by Demailly. A number of properties of the boundary measures are proved, and we describe how boundary values of bounded plurisubharmonic functions can be associated to the boundary measures.In the second paper, we study an ordering of measures induced by plurisubharmonic functions. This ordering arises naturally in connection with problems related to negative plurisubharmonic functions. We study maximality with respect to the ordering and a related notion of minimality for certain plurisubharmonic functions. The ordering is then applied to problems of weak*-convergence of measures, in particular Monge-Ampère measures.In the third paper we continue the work on boundary values in a more general setting than in Paper I. We approximate measures living on the boundary with measures on the interior of the domain, and present conditions on the approximation which makes the procedure suitable for defining boundary values of certain plurisubharmonic functions.

Place, publisher, year, edition, pages
Umeå: Umeå University, Department of Mathematics , 2009.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 43
Keyword [en]
Plurisubharmonic functions, boundary measures, boundary values, complex Monge-Ampère operator, weak*-convergence
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-29870ISBN: 978-91-7264-906-4 (print)OAI: oai:DiVA.org:umu-29870DiVA: diva2:278356
Public defence
2009-12-18, MA121, MIT-huset, Umeå universitet, 901 87 Umeå, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2009-11-27 Created: 2009-11-25 Last updated: 2009-11-27Bibliographically approved
List of papers
1. Monge-Ampère boundary measures
Open this publication in new window or tab >>Monge-Ampère boundary measures
2009 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 96, no 2, 175-196 p.Article in journal (Refereed) Published
Abstract [en]

We study swept-out Monge–Ampère measures of plurisubharmonic functions and boundary values related to those measures.

Identifiers
urn:nbn:se:umu:diva-19730 (URN)
Note
Tidigare version publicerad i rapportserie vid Institutionen för matematik och matematisk statistik, Umeå universitet: Research report in Mathematics (Umeå), ISSN: 1653-0810; 2007:6Available from: 2009-03-10 Created: 2009-03-10 Last updated: 2017-12-13
2. An ordering of measures induced by plurisubharmonic functions
Open this publication in new window or tab >>An ordering of measures induced by plurisubharmonic functions
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We study an ordering of measures induced by plurisubharmonic functions. This ordering arises naturally in connection with problems related to negative plurisubharmonic functions. We study maximality with respect to the ordering and a related notion of minimality for certain plurisubharmonic functions. The ordering is then applied to the problem of weak*-convergence of measures, in particular Monge-Ampère measures.

Keyword
plurisubharmonic functions, parital order, weak*-convergence
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-27764 (URN)
Available from: 2009-11-20 Created: 2009-11-19 Last updated: 2009-11-24Bibliographically approved
3. On boundary values of plurisubharmonic functions
Open this publication in new window or tab >>On boundary values of plurisubharmonic functions
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper we describe how boundary values of bounded plurisubharmonic functions can be defined in terms of measures with support on the boundary. We do this by approximating the boundary measures with measures on the interior of the domain, and present conditions on the approximation which makes the procedure suitable for defining boundary values of certain plurisubharmonic functions.

Keyword
plurisubharmonic functions, boundary values
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-27777 (URN)
Projects
plurisubharmonic functions, boundary values
Available from: 2009-11-24 Created: 2009-11-19 Last updated: 2009-11-24Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • Other locale
More languages
Output format
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