Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Full Laplace spectrum of distance spheres in symmetric spaces of rank
  one   We use Lie-theoretic methods to explicitly compute the full spectrum of the
Laplace--Beltrami operator on homogeneous spheres which occur as geodesic
distance spheres in (compact or noncompact) symmetric spaces of rank one, and
provide a single unified formula for all cases. As an application, we find all
resonant radii for distance spheres in the compact case, i.e., radii where
there is bifurcation of embedded constant mean curvature spheres, and show that
distance spheres are stable and locally rigid in the noncompact case.

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The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex