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A comparison principle for the complex Monge-Ampère operator in Cegrell's classes and applications
Department of Mathematics, Hanoi University of Education, Dai hoc Su Pham Hanoi, Cau Giay, Hanoi, Vietnam.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2009 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 361, 5539-5554 p.Article in journal (Refereed) Published
Abstract [en]

In this article we will first prove a result about the convergence in capacity. Next we will obtain a general decomposition theorem for complex Monge-Ampère measures which will be used to prove a comparison principle for the complex Monge-Ampère operator.

Place, publisher, year, edition, pages
2009. Vol. 361, 5539-5554 p.
Keyword [en]
Complex Monge-Amp\`ere operator, plurisubharmonic function
Identifiers
URN: urn:nbn:se:umu:diva-2981DOI: 10.1090/S0002-9947-09-04730-8OAI: oai:DiVA.org:umu-2981DiVA: diva2:141386
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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