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

Benedikt Steinar Magnússon

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.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15228

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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