Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Near-Constant Mean Curvature Solutions of the Einstein Constraint
  Equations with Non-Negative Yamabe Metrics   We show that sets of conformal data on closed manifolds with the metric in
the positive or zero Yamabe class, and with the gradient of the mean curvature
function sufficiently small, are mapped to solutions of the Einstein constraint
equations. This result extends previous work which required the conformal
metric to be in the negative Yamabe class, and required the mean curvature
function to be nonzero.

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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin