Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A rigidity criterion for non-convex polyhedra   Let $P$ be a (non necessarily convex) embedded polyhedron in $\R^3$, with its
vertices on an ellipsoid. Suppose that the interior of $P$ can be decomposed
into convex polytopes without adding any vertex. Then $P$ is infinitesimally
rigid. More generally, let $P$ be a polyhedron bounding a domain which is the
union of polytopes $C_1, ..., C_n$ with disjoint interiors, whose vertices are
the vertices of $P$. Suppose that there exists an ellipsoid which contains no
vertex of $P$ but intersects all the edges of the $C_i$. Then $P$ is
infinitesimally rigid. The proof is based on some geometric properties of
hyperideal hyperbolic polyhedra.

11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph