Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $W^{1,p}$-metrics and conformal metrics with $L^{n/2}$-bounded scalar
  curvature   A $W^{1,p}$-metric on an $n$-dimensional closed Riemannian manifold naturally
induces a distance function, provided $p$ is sufficiently close to $n$. If a
sequence of metrics $g_k$ converges in $W^{1,p}$ to a limit metric $g$, then
the corresponding distance functions $d_{g_k}$ subconverge to a limit distance
function $d$, which satisfies $d\le d_g$.
  As an application, we show that the above convergence result applies to a
sequence of conformal metrics with $L^{n/2}$-bounded scalar curvatures, under
certain geometric assumptions. In particular, in this special setting, the
limit distance function $d$ actually coincides with $d_{g}$.

11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg