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Arkiv för Matematik

, Volume 49, Issue 2, pp 383–399 | Cite as

Extremal ω-plurisubharmonic functions as envelopes of disc functionals

  • Benedikt Steinar Magnússon
Article

Abstract

For each closed, positive (1,1)-current ω on a complex manifold X and each ω-upper semicontinuous function φ on X we associate a disc functional and prove that its envelope is equal to the supremum of all ω-plurisubharmonic functions dominated by φ. This is done by reducing to the case where ω has a global potential. Then the result follows from Poletsky’s theorem, which is the special case ω=0. Applications of this result include a formula for the relative extremal function of an open set in X and, in some cases, a description of the ω-polynomial hull of a set.

Keywords

Complex Manifold Local Potential Plurisubharmonic Function Riesz Potential Reduction Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Institut Mittag-Leffler 2010

Authors and Affiliations

  1. 1.Science InstituteUniversity of IcelandReykjavikIceland

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