Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gluing Scalar-Flat Manifolds with Vanishing Mean Curvature on the
  Boundary   We establish a gluing theorem for solutions of a Yamabe problem for manifolds
with boundary studied by Escobar in the 90's. Given two scalar-flat Riemannian
manifolds whose boundary has zero mean curvature and sharing a submanifold $K$,
we produce the generalized connected sum along $K$. On this third manifold we
produce a family of scalar-flat metrics with small, constant mean curvature on
the boundary which are close to the original metrics in the $C^2$ sense. Under
extra geometric conditions on the original manifolds, we can arrange for this
family to also have vanishing mean curvature on the boundary.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics