Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of vacuum initial data by the conformally covariant split
  system   Using the implicit function theorem, we prove existence of solutions of the
so-called conformally covariant split system on compact 3-dimensional
Riemannian manifolds. They give rise to non-Constant Mean Curvature (non-CMC)
vacuum initial data for the Einstein equations. We investigate the conformally
covariant split system defined on compact manifolds with or without boundaries.
In the former case, the boundary corresponds to an apparent horizon in the
constructed initial data. The case with a cosmological constant is then
considered separately. Finally, to demonstrate the applicability of the
conformal covariant split system in numerical studies, we provide numerical
examples of solutions on manifolds $\mathbb S^1 \times \mathbb S^2$ and
$\mathbb S^1 \times \mathbb T^2$.

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat