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Partial pluricomplex energy and integrability exponents of plurisubharmonic functions
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.
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2009 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 222, no 6, 2036-2058 p.Article in journal (Refereed) Published
Abstract [en]

We first prove a quantitative estimate of the volume of the sublevel sets of a plurisubharmonic function in a hyperconvex domain with boundary values 0 (in a quite general sense) in terms of its Monge–Ampère mass in the domain. Then we deduce a sharp sufficient condition on the Monge–Ampère mass of such a plurisubharmonic function φ for exp(−2φ) to be globally integrable as well as locally integrable.

Place, publisher, year, edition, pages
2009. Vol. 222, no 6, 2036-2058 p.
Keyword [en]
Plurisubharmonic functions; Pluricomplex Monge–Ampère energy; Volume of the sublevel sets; Exponents of integrability; Log canonical thresholds
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-25712OAI: oai:DiVA.org:umu-25712DiVA: diva2:233345
Available from: 2009-08-31 Created: 2009-08-31 Last updated: 2017-12-13Bibliographically approved

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