2013/12/02 by Jun Nonaka, Nonaka, Jun · 1 citation
Mathematics · #20F55 #51F15 #57M50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:20F55 #msc:51F15 #msc:57M50
paper · pdf · doi:10.48550/arxiv.1312.0380
23 pages
arxiv created 2014/12/22 · arxiv updated 2014/12/23
As was pointed out by Nikulin [8] and Vinberg [10], a right-angled polyhedron of finite volume in 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.