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arXiv · 0806.4850

Weighted pluricomplex energy

Slimane Benelkourchi
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Abstract

We study the complex Monge-Ampre operator on the classes of finite pluricomplex energy $\mathcal{E}_χ(Ω)$ in the general case ($χ(0)=0$ 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 $\mathcal{E}χ(Ω).$

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Slimane Benelkourchi. 2009-03-15. Weighted pluricomplex energy. https://arxiv.org/abs/0806.4850

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