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

Benedikt Steinar Magnusson

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

Complex Variables 2011-07-20 v2

Authors: Benedikt Steinar Magnusson

Abstract

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.

Keywords

omega-plurisubharmonic functions disc functionals Poletsky disc envelope formula complex manifold positive closed currents

Cite

@article{arxiv.1103.4297,
  title  = {Extremal omega-plurisubharmonic functions as envelopes of disc functionals - Generalization and applications to the local theory},
  author = {Benedikt Steinar Magnusson},
  journal= {arXiv preprint arXiv:1103.4297},
  year   = {2011}
}

Comments

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

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

Abstract

Keywords

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