Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalar Flat Compactifications Of Poincar{\'e}-einstein Manifolds And
  Applications   We derive an integral inequality between the mean curvature and the scalar
curvature of the boundary of any scalar flat conformal compactifications of
Poincar{\'e}-Einstein manifolds. As a first consequence , we obtain a sharp
lower bound for the first eigenvalue of the conformal half-Laplacian of the
boundary of such manifolds. Secondly, a new upper bound for the renormalized
volume is given in the four dimensional setting. Finally, some estimates on the
first eigenvalues of Dirac operators are also deduced.

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The categories of this paper are: hep-th
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys