Extremal $\omega$-plurisubharmonic functions as envelopes of disc functionals: generalization and applications to the local theory

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Dec 2012Embargo end date: 01 Jan 2011Publisher:Det Kgl. Bibliotek/Royal Danish LibraryJournal:MATHEMATICA SCANDINAVICA, volume 111, page 296 (issn: 0025-5521, eissn: 1903-1807,

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Authors: Magnusson, Benedikt Steinar;

doi: 10.7146/math.scand.a-15228 , 10.48550/arxiv.1103.4297

arXiv: 1103.4297

Extremal $\omega$-plurisubharmonic functions as envelopes of disc functionals: generalization and applications to the local theory

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Abstract

We generalize the Poletsky disc envelope formula for the function $\sup \{u\in \mathcal{PSH}(X,\omega); u\leq \phi\}$ on any complex manifold $X$ to the case where the real $(1,1)$-current $\omega=\omega_1-\omega_2$ is the difference of two positive closed $(1,1)$-currents and $\varphi$ is the difference of an $\omega_1$-upper semicontinuous function and a plurisubharmonic function.

Keywords

Mathematics - Complex Variables, 32U05, 32U40, FOS: Mathematics, Complex Variables (math.CV)

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