Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sums of magnetic eigenvalues are maximal on rotationally symmetric
  domains   The sum of the first n energy levels of the planar Laplacian with constant
magnetic field of given total flux is shown to be maximal among triangles for
the equilateral triangle, under normalization of the ratio (moment of
inertia)/(area)^3 on the domain. The result holds for both Dirichlet and
Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary
conditions too. The square similarly maximizes the eigenvalue sum among
parallelograms, and the disk maximizes among ellipses. More generally, a domain
with rotational symmetry will maximize the magnetic eigenvalue sum among all
linear images of that domain. These results are new even for the ground state
energy (n=1).

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas