Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Einstein-scalar field constraints on asymptotically Euclidean
  manifolds   We use the conformal method to obtain solutions of the Einstein-scalar field
gravitational constraint equations. Handling scalar fields is a bit more
challenging than handling matter fields such as fluids, Maxwell fields or
Yang-Mills fields, because the scalar field introduces three extra terms into
the Lichnerowicz equation, rather than just one. Our proofs are constructive
and allow for arbitrary dimension (>2) as well as low regularity initial data.

33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con