Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density problems for second order Sobolev spaces and cut-off functions
  on manifolds with unbounded geometry   We consider complete non-compact manifolds with either a sub-quadratic growth
of the norm of the Riemann curvature, or a sub-quadratic growth of both the
norm of the Ricci curvature and the squared inverse of the injectivity radius.
We show the existence on such a manifold of a distance-like function with
bounded gradient and mild growth of the Hessian. As a main application, we
prove that smooth compactly supported functions are dense in $W^{2,p}$. The
result is improved for $p=2$ avoiding both the upper bound on the Ricci tensor,
and the injectivity radius assumption. As further applications we prove new
disturbed Sobolev and Calder\'on-Zygmund inequalities on manifolds with
possibly unbounded curvature and highlight consequences about the validity of
the full Omori-Yau maximum principle for the Hessian.

11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn