Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex Monge-Amp\`ere equation for measures supported on real
  submanifolds   Let $(X,\omega)$ be a compact $n$-dimensional K\"ahler manifold on which the
integral of $\omega^n$ is $1$. Let $K$ be an immersed real $\mathcal{C}^3$
submanifold of $X$ such that the tangent space at any point of $K$ is not
contained in any complex hyperplane of the (real) tangent space at that point
of $X.$ Let $\mu$ be a probability measure compactly supported on $K$ with
$L^p$ density for some $p>1.$ We prove that the complex Monge-Amp\`ere equation
$(dd^c \varphi + \omega)^n=\mu$ has a H\"older continuous solution.

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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat