Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A compactness theorem on Branson's $Q$-curvature equation   Let $(M, g)$ be a closed Riemannian manifold of dimension $5$. Assume that
$(M, g)$ is not conformally equivalent to the round sphere. If the scalar
curvature $R_g\geq 0$ and the $Q$-curvature $Q_g\geq 0$ on $M$ with $Q_g(p)>0$
for some point $p\in M$, we prove that the set of metrics in the conformal
class of $g$ with prescribed constant positive $Q$-curvature is compact in
$C^{4, \alpha}$ for any $0 <\alpha < 1$. We also give some estimates for
dimension $6$ and $7$.

37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg