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October 2011 Extremal ω-plurisubharmonic functions as envelopes of disc functionals
Benedikt Steinar Magnússon
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Ark. Mat. 49(2): 383-399 (October 2011). DOI: 10.1007/s11512-010-0128-y


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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Benedikt Steinar Magnússon. "Extremal ω-plurisubharmonic functions as envelopes of disc functionals." Ark. Mat. 49 (2) 383 - 399, October 2011.


Received: 8 June 2009; Revised: 24 March 2010; Published: October 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1264.32028
MathSciNet: MR2826950
Digital Object Identifier: 10.1007/s11512-010-0128-y

Rights: 2010 © Institut Mittag-Leffler


Vol.49 • No. 2 • October 2011
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