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.
Published
2012-12-01
How to Cite
Magnússon, B. S. (2012). Extremal $\omega$-plurisubharmonic functions as envelopes of disc functionals: generalization and applications to the local theory. MATHEMATICA SCANDINAVICA, 111(2), 296-319. https://doi.org/10.7146/math.scand.a-15228
Section
Articles