Arkiv för Matematik
- Ark. Mat.
- Volume 49, Number 2 (2011), 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.
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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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. https://projecteuclid.org/euclid.afm/1485907145