Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cauchy-Riemann inequalities on 2-spheres of $\mathbb{R}^7$   We prove that an integral Cauchy-Riemann inequality holds for any pair of
smooth functions $(f,h)$ on the 2-sphere $\mathbb{S}^2$, and equality holds iff
$f$ and $h$ are related $\lambda_1$-eigenfunctions. We extend such inequality
to 4-tuples of functions, only valid on the $L^2$-orthogonal complement of a
suitable nonzero finite dimensional space of functions. As a consequence we
prove that 2-spheres are not $\Omega$-stable surfaces with parallel mean
curvature in $\mathbb{R}^7$ for the associative calibration $\Omega$.

34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-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
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th