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arXiv · 0906.0902

Extremal omega-plurisubharmonic functions as envelopes of disc functionals

Benedikt Steinar Magnusson
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Abstract

For each closed, positive (1,1)-current ωon a complex manifold X and each ω-upper semicontinuous function ϕon 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 ωhas 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 Magnusson. 2010-04-11. Extremal omega-plurisubharmonic functions as envelopes of disc functionals. https://arxiv.org/abs/0906.0902

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