Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-axially symmetric solutions of a mean field equation on
  $\mathbb{S}^2$   We prove the existence of a family of blow-up solutions of a mean field
equation on sphere. The solutions blow up at four points where the minimum
value of a potential energy function (involving the Green's function) is
attained. The four blow-up points form a regular tetrahedron. Moreover, the
solutions we build have a group of symmetry $T_d$ which is isomorphic to the
symmetric group $S_4$. Other families of solutions can be similarly constructed
with blow-up points at the vertices of equilateral triangles on a great circle
or other inscribed platonic solids (cubes, octahedrons, icosahedrons and
dodecahedrons). All of these solutions have the symmetries of the corresponding
configuration, while they are non-axially symmetric.

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The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga