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On the convergence in capacity on compact Kähler manifolds and its applications
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2008 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 136, no 6, p. 2007-2018Article in journal (Refereed) Published
Abstract [en]

The main aim of the present note is to study the convergence inCX,ω on a compact Kahler mainfold X. The obtained results are used to studyglobal extremal functions and describe the ω-pluripolar hull of an ω-pluripolarsubset in X.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2008. Vol. 136, no 6, p. 2007-2018
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-2986OAI: oai:DiVA.org:umu-2986DiVA, id: diva2:141391
Available from: 2008-02-26 Created: 2008-02-26 Last updated: 2018-03-15Bibliographically 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. p. 19
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 40
Keywords
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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