Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vanishing Estimates for Liouville equation with quantized singularities   In this article we continue with the research initiated in our previous work
on singular Liouville equations with quantized singularity. The main goal of
this article is to prove that as long as the bubbling solutions violate the
spherical Harnack inequality near a singular source, the first derivatives of
coefficient functions must tend to zero.

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The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn