Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted pluricomplex energy   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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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc