Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isoperimetric control of the Steklov spectrum   Let N be a complete Riemannian manifold of dimension n+1 whose Riemannian
metric g is conformally equivalent to a metric with non-negative Ricci
curvature. The normalized Steklov eigenvalues of a bounded domain in N are
bounded above in terms of the isoperimetric ratio of the domain. Consequently,
the normalized Steklov eigenvalues of a bounded domain in Euclidean space,
hyperbolic space or a standard hemisphere are uniformly bounded above. On a
compact surface with boundary, the normalized Steklov eigenvalues are uniformly
bounded above in terms of the genus. We also obtain a relationship between the
Steklov eigenvalues of a domain and the eigenvalues of the Laplace-Beltrami
operator on its bounding hypersurface.

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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph