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December 2015 The Number of Cusps of Right-angled Polyhedra in Hyperbolic Spaces
Jun NONAKA
Tokyo J. Math. 38(2): 539-560 (December 2015). DOI: 10.3836/tjm/1452806056

Abstract

As was pointed out by Nikulin [8] and Vinberg [10], a right-angled polyhedron of finite volume in the hyperbolic $n$-space $\mathbf{H}^n$ 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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Jun NONAKA. "The Number of Cusps of Right-angled Polyhedra in Hyperbolic Spaces." Tokyo J. Math. 38 (2) 539 - 560, December 2015. https://doi.org/10.3836/tjm/1452806056

Information

Published: December 2015
First available in Project Euclid: 14 January 2016

zbMATH: 1341.51014
MathSciNet: MR3448873
Digital Object Identifier: 10.3836/tjm/1452806056

Subjects:
Primary: 20F55
Secondary: 51F15, 57M50

Rights: Copyright © 2015 Publication Committee for the Tokyo Journal of Mathematics

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Vol.38 • No. 2 • December 2015
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