Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The number of cusps of right-angled polyhedra in hyperbolic spaces   As was pointed out by Nikulin [8] and Vinberg [10], a right-angled polyhedron
of finite volume in hyperbolic n-space $\mathbb{H}^n$ has at least one cusp for
$n\geq 5$. We obtain non-trivial lower bounds on the number of cusps of such
polyhedra. For example, right-angled polyhedra of finite volume must have at
least three cusps for $n=6$. Our theorem also says that the higher the
dimension of a right-angled polyhedron becomes, the more cusps it must have.

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The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: eess