Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monge-Amp\`ere operators on compact K\"ahler manifolds   We study the complex Monge-Amp\` ere operator on compact K\"ahler manifolds.
We give a complete description of its range on the set of
$\omega-$plurisubharmonic functions with $L^2$ gradient and finite self energy,
generalizing to this compact setting results of U.Cegrell from the local
pluripoltential theory. We give some applications to complex dynamics and to
the existence of K\"ahler-Einstein metrics on singular manifolds.

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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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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: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph