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Boundary values of plurisubharmonic functions and related topics
Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
2009 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Umeå: Umeå University, Department of Mathematics , 2009.
Serie
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 43
Nyckelord [en]
Plurisubharmonic functions, boundary measures, boundary values, complex Monge-Ampère operator, weak*-convergence
Nationell ämneskategori
Matematisk analys
Forskningsämne
matematik
Identifikatorer
URN: urn:nbn:se:umu:diva-29870ISBN: 978-91-7264-906-4 (tryckt)OAI: oai:DiVA.org:umu-29870DiVA, id: diva2:278356
Disputation
2009-12-18, MA121, MIT-huset, Umeå universitet, 901 87 Umeå, Umeå, 10:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2009-11-27 Skapad: 2009-11-25 Senast uppdaterad: 2018-06-08Bibliografiskt granskad
Delarbeten
1. Monge-Ampère boundary measures
Öppna denna publikation i ny flik eller fönster >>Monge-Ampère boundary measures
2009 (Engelska)Ingår i: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 96, nr 2, s. 175-196Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

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

Identifikatorer
urn:nbn:se:umu:diva-19730 (URN)
Anmärkning
Tidigare version publicerad i rapportserie vid Institutionen för matematik och matematisk statistik, Umeå universitet: Research report in Mathematics (Umeå), ISSN: 1653-0810; 2007:6Tillgänglig från: 2009-03-10 Skapad: 2009-03-10 Senast uppdaterad: 2018-06-09
2. An ordering of measures induced by plurisubharmonic functions
Öppna denna publikation i ny flik eller fönster >>An ordering of measures induced by plurisubharmonic functions
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
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.

Nyckelord
plurisubharmonic functions, parital order, weak*-convergence
Nationell ämneskategori
Matematisk analys
Forskningsämne
matematik
Identifikatorer
urn:nbn:se:umu:diva-27764 (URN)
Tillgänglig från: 2009-11-20 Skapad: 2009-11-19 Senast uppdaterad: 2018-06-08Bibliografiskt granskad
3. On boundary values of plurisubharmonic functions
Öppna denna publikation i ny flik eller fönster >>On boundary values of plurisubharmonic functions
(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
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.

Nyckelord
plurisubharmonic functions, boundary values
Nationell ämneskategori
Matematisk analys
Forskningsämne
matematik
Identifikatorer
urn:nbn:se:umu:diva-27777 (URN)
Projekt
plurisubharmonic functions, boundary values
Tillgänglig från: 2009-11-24 Skapad: 2009-11-19 Senast uppdaterad: 2018-06-08Bibliografiskt granskad

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Kemppe, Berit

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