Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity of configurations of balls and points in the $N$-sphere   We answer two questions of Beardon and Minda that arose from their study of
the conformal symmetries of circular regions in the complex plane. We show that
a configuration of closed balls in the $N$-sphere is determined up to
M\"{o}bius transformations by the signed inversive distances between pairs of
its elements, except when the boundaries of the balls have a point in common,
and that a configuration of points in the $N$-sphere is determined by the
absolute cross-ratios of 4-tuples of its elements. The proofs use the
hyperboloid model of hyperbolic $(N+1)$-space.

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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th