Extremal $ω$-plurisubharmonic functions as envelopes of disc functionals: generalization and applications to the local theory - Magnússon, Benedikt Steinar (MATHEMATICA SCANDINAVICA, 2012)
We generalize the Poletsky disc envelope formula for the function $\sup \{u\in \mathcal{PSH}(X,ω); u≤ φ\}$ on any complex manifold $X$ to the case where the real $(1,1)$-current $ω=ω_1-ω_2$ is the difference of two positive closed $(1,1)$-currents and $φ$ is the difference of an $ω_1$-upper semicontinuous function and a plurisubharmonic function.