Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The complex Monge-Amp\`ere type equation on compact Hermitian manifolds
  and Applications   We prove the existence and uniqueness of continuous solutions to the complex
Monge-Amp\`ere type equation with the right hand side in $L^p$, $p>1$, on
compact Hermitian manifolds. Next, we generalise results of Eyssidieux, Guedj
and Zeriahi \cite{EGZ09, EGZ11} to compact Hermitian manifolds which {\em a
priori} are not in the Fujiki class. These generalisations lead to a number of
applications: we obtain partial results on a conjecture of Tosatti and Weinkove
\cite{TW12a} and on a weak form of a conjecture of Demailly and Paun
\cite{DP04}.

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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
1
The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ