Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robin and Steklov isospectral manifolds   We use two of the most fruitful methods for constructing isospectral
manifolds, the Sunada method and the torus action method, to construct
manifolds whose Dirichlet-to-Neumann operators are isospectral at all
frequencies. The manifolds are also isospectral for the Robin boundary value
problem for all choices of Robin parameter. As in the sloshing problem, we can
also impose mixed Dirichlet-Neumann conditions on parts of the boundary. Among
the examples we exhibit are Steklov isospectral flat surfaces with boundary,
planar domains with isospectral sloshing problems, and Steklov isospectral
metrics on balls of any dimension greater than 5. In particular, the latter are
the first examples of Steklov isospectral manifolds of dimension greater than 2
that have connected boundaries.

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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys