Abstract
As was pointed out by Nikulin [8] and Vinberg [10], a right-angled polyhedron of finite volume in the hyperbolic n-space Hn has at least one cusp for n ≥ 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.
Original language | English |
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Pages (from-to) | 539-560 |
Number of pages | 22 |
Journal | Tokyo Journal of Mathematics |
Volume | 38 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2015 Dec |
Keywords
- Combinatorics
- Cusp
- Hyperbolic space
- Right-angled polyhedron
ASJC Scopus subject areas
- Mathematics(all)