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

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

2011-03-22

arxiv.org/abs/1103.4297v2

Mathematics

Complex Variables

24 pages; minor corrections and notation for the extension over sing(\omega) clarified

Scientific paper

We generalize the Poletsky disc envelope formula for the function $\sup \{u
\in \PSH(X,\omega) ; u\leq \phi\}$ 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 $\phi$ is the difference of an
$\omega_1$-upper semicontinuous function and a plurisubharmonic function.

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