Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monotonicity of the $p$-Green functions   On a complete $p$-nonparabolic $3$-dimensional manifold with non-negative
scalar curvature and vanishing second homology, we establish a sharp
monotonicity formula for the proper $p$-Green function along its level sets for
$1<p<3$. This can be viewed as a generalization of the recent result by
Munteanu-Wang \cite{MunteanuWang2021} in the case of $p=2$. No smoothness
assumption is made on the $p$-Green function when $1<p\leq 2$. Several rigidity
results are also proven.

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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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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: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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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: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con