Paper detail

Extremal omega-plurisubharmonic functions as envelopes of disc functionals - Generalization and applications to the local theory

We generalize the Poletsky disc envelope formula for the function $\sup \{u \in \PSH(X,ω) ; u\leq ϕ\}$ 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.