Arkiv för Matematik

, Volume 49, Issue 2, pp 383–399

Extremal ω-plurisubharmonic functions as envelopes of disc functionals



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.


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© Institut Mittag-Leffler 2010

Authors and Affiliations

  1. 1.Science InstituteUniversity of IcelandReykjavikIceland

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