As was pointed out by Nikulin  and Vinberg , 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.
ASJC Scopus subject areas
- 数学 (全般)