Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The smooth Riemannian extension problem: completeness   By means of a general gluing and conformal-deformation construction, we prove
that any smooth, metrically complete Riemannian manifold with smooth boundary
can be realized as a closed domain into a smooth, geodesically complete
Riemannan manifold without boundary. Applications to Sobolev spaces, Nash
embedding and local extensions with strict curvature bounds are presented.

27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th