Weighted pluricomplex energy

Details Weighted pluricomplex energy Weighted pluricomplex energy

2008-06-30

arxiv.org/abs/0806.4850v2

Mathematics

Complex Variables

Contrary to what we claimed in the previous version, in Theorem 5.1 we generalize some Theorem of Urban Cegrell but we do not

Scientific paper

We study the complex Monge-Ampre operator on the classes of finite pluricomplex energy $\mathcal{E}_\chi (\Omega)$ in the general case ($\chi(0)=0$ 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 $(dd^c \cdot)^n$ on the classes $\mathcal{E}\chi(\Omega).$

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