Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the higher order conformal covariant operators on the sphere   We will show that in the conformal class of the standard metric $g_{S^n}$ on
$S^n$, the scaling invariant functional
$(\mu_g(S^n))^{\frac{2m-n}{n}}\int_{S^n}Q_{2m,g}d\mu_g$ maximizes at $g_{S^n}$
when $n$ is odd and $m=\frac{n+1}{2}$ or $\frac{n+3}{2}$. For $n$ odd and
$m\geq\frac{n+5}{2}$, $g_{S^n}$ is not stable and the functional has no local
maximizer. Here $Q_{2m,g}$ is the $2m$th order $Q $-curvature.

1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat