Arkiv för Matematik

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  • Volume 49, Number 2 (2011), 383-399.

Extremal ω-plurisubharmonic functions as envelopes of disc functionals

Benedikt Steinar Magnússon

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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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Ark. Mat., Volume 49, Number 2 (2011), 383-399.

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

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2010 © Institut Mittag-Leffler


Magnússon, Benedikt Steinar. Extremal ω -plurisubharmonic functions as envelopes of disc functionals. Ark. Mat. 49 (2011), no. 2, 383--399. doi:10.1007/s11512-010-0128-y.

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