Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compactness of solutions to the Yamabe problem. III   For a sequence of blow up solutions of the Yamabe equation on non-locally
confonformally flat compact Riemannian manifolds of dimension 10 or 11, we
establish sharp estimates on its asymptotic profile near blow up points as well
as sharp decay estimates of the Weyl tensor and its covariant derivatives at
blow up points. If the Positive Mass Theorem held in dimensions 10 and 11,
these estimates would imply the compactness of the set of solutions of the
Yamabe equation on such manifolds.

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The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat