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

Abstract

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 $\omega ={\omega }_1-{\omega }_2$ 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.

arXiv comment24 pages; minor corrections and notation for the extension over sing(ω) clarified