Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Sobolev-Poincare inequality of CR-manifolds   The purpose is to study the CR-manifold with a contact structure conformal to
the Heisenberg group. In our previous work \cite{WY}, we have proved that if
the $Q'$-curvature is nonnegative, and the integral of $Q'$-curvature is below
the dimensional bound $c_1'$, then we have the isoperimetric inequality. In
this paper, we manage to drop the condition on the nonnegativity of the
$Q'$-curvature. We prove that the volume form $e^{4u}$ is a strong $A_\infty$
weight. As a corollary, we prove the Sobolev-Poincar\'e inequality on a class
of CR-manifolds with integrable $Q'$-curvature.

4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph