Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On first and second eigenvalues of Riesz transforms in spherical and
  hyperbolic geometries   In this note we prove an analogue of the Rayleigh-Faber-Krahn inequality,
that is, that the geodesic ball is a maximiser of the first eigenvalue of some
convolution type integral operators, on the sphere $\mathbb{S}^{n}$ and on the
real hyperbolic space $\mathbb{H}^{n}$. It completes the study of such question
for complete, connected, simply connected Riemannian manifolds of constant
sectional curvature. We also discuss an extremum problem for the second
eigenvalue on $\mathbb{H}^{n}$ and prove the Hong-Krahn-Szeg\"{o} type
inequality. The main examples of the considered convolution type operators are
the Riesz transforms with respect to the geodesic distance of the space.

33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th