Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compactness Theorem of Complete k-Curvature Manifolds with Isolated
  Singularities   In this paper we prove that the set of metrics conformal to the standard
metric on $\mathbb{S}^{n}\backslash\{p_{1},\cdots,p_{l}\}$ is locally compact
in $C^{m,\alpha}$ topology for any $m>0$, whenever the metrics have constant
$\sigma_{k}$ curvature and the $k$-Dilational Pohozaev invariants have positive
lower bound for $k<n/2$. Here the $k$-Dilational Pohozaev invariants come from
the Kazdan-Warner type identity for the $\sigma_{k}$ curvature, which is
derived by Viaclovsky \cite{Viac2000} and Han \cite{H1}. When $k=1$, Pollack
\cite{Pollack} proved the compactness results for the complete metrics of
constant positive scalar curvature on
$\mathbb{S}^{n}\backslash\{p_{1},\cdots,p_{l}\}$.

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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: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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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: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex