Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polarization tensor vanishing structure of general shape: Existence for
  small perturbations of balls   The polarization tensor is a geometric quantity associated with a domain. It
is a signature of the small inclusion's existence inside a domain and used in
the small volume expansion method to reconstruct small inclusions by boundary
measurements. In this paper, we consider the question of the polarization
tensor vanishing structure of general shape. The only known examples of the
polarization tensor vanishing structure are concentric disks and balls. We
prove, by the implicit function theorem on Banach spaces, that a small
perturbation of a ball can be enclosed by a domain so that the resulting
inclusion of the core-shell structure becomes polarization tensor vanishing.
The boundary of the enclosing domain is given by a sphere perturbed by
spherical harmonics of degree zero and two. This is a continuation of the
earlier work \cite{KLS2D} for two dimensions.

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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio