English

Weighted pluricomplex energy

Complex Variables 2009-03-15 v2

Abstract

We study the complex Monge-Ampre operator on the classes of finite pluricomplex energy Eχ(Ω)\mathcal{E}_\chi (\Omega) in the general case (χ(0)=0\chi(0)=0 i.e. the total Monge-Ampre mass may be infinite). We establish an interpretation of these classes in terms of the speed of decrease of the capacity of sublevel sets and give a complete description of the range of the operator (ddc)n(dd^c \cdot)^n on the classes Eχ(Ω).\mathcal{E}\chi(\Omega).

Cite

@article{arxiv.0806.4850,
  title  = {Weighted pluricomplex energy},
  author = {Slimane Benelkourchi},
  journal= {arXiv preprint arXiv:0806.4850},
  year   = {2009}
}

Comments

Contrary to what we claimed in the previous version, in Theorem 5.1 we generalize some Theorem of Urban Cegrell but we do not give a new proof. To appear in Potenial Analysis

R2 v1 2026-06-21T10:55:48.735Z