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Monge-Ampère measures on pluripolar sets
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2009 (English)In: Journal des Mathématiques Pures et Appliquées, ISSN 0021-7824, E-ISSN 1776-3371, Vol. 92, no 6, 613-627 p.Article in journal (Refereed) Published
Abstract [en]

In this article we solve the complex Monge–Ampère problem for measures with large singular part. This result generalizes classical results by Demailly, Lelong and Lempert a.o., who considered singular parts carried on discrete sets. By using our result we obtain a generalization of Kołodziej's subsolution theorem. More precisely, we prove that if a non-negative Borel measure is dominated by a complex Monge–Ampère measure, then it is a complex Monge–Ampère measure.

Place, publisher, year, edition, pages
2009. Vol. 92, no 6, 613-627 p.
Keyword [en]
Complex Monge–Ampère operator, Dirichlet problem, Pluripolar set, Plurisubharmonic function
Identifiers
URN: urn:nbn:se:umu:diva-2983DOI: 10.1016/j.matpur.2009.06.001OAI: oai:DiVA.org:umu-2983DiVA: diva2:141388
Available from: 2008-02-26 Created: 2008-02-26 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Dirichlet's problem in Pluripotential Theory
Open this publication in new window or tab >>Dirichlet's problem in Pluripotential Theory
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we focus on Dirichlet's problem for the complex Monge-Ampère equation. That is, for a given non-negative Radon measure µ we are interested in the conditions under which there exists a plurisubharmonic function u such that (ddcu)n=µ, where (ddc)n is the complex Monge-Ampère operator. If this function u exists, then can it be chosen with given boundary values? Is this solution uniquely determined within a given class of functions?

Place, publisher, year, edition, pages
Umeå: Matematik och matematisk statistik, 2008. 19 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 40
Keyword
Complex Monge-Ampère operator, currents, Dirichlet problem, pluripotential theory, plurisubharmonic function, subextension
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-1562 (URN)978-91-7264-443-4 (ISBN)
Public defence
2008-03-19, MA121, MIT, 901 87, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2008-02-26 Created: 2008-02-26 Last updated: 2009-06-17Bibliographically approved

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Åhag, PerCegrell, UrbanPhạm, Hoàng Hiệp
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