Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetric inequality for the third eigenvalue of the
  Laplace-Beltrami operator on $\mathbb S^2$   We prove an Hersch's type isoperimetric inequality for the third positive
eigenvalue on $\mathbb S^2$. Our method builds on the theory we developped to
construct extremal metrics on Riemannian surfaces in conformal classes for any
eigenvalue.

11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th