On right-angled reflection groups in hyperbolic spaces

• Autores: Leonid Potyagailo, Ernest Vinberg
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 80, Nº 1, 2005, págs. 63-73
• Idioma: inglés
• DOI: 10.4171/cmh/4
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• Resumen

  • We show that the right-angled hyperbolic polyhedra of finite volume in the hyperbolic space $\Bbb H^n$ may only exist if $n\leq 14.$ We also provide a family of such polyhedra of dimensions $n=3,4,...,8$. We prove that for $n=3,4$ the members of this family have the minimal total number of hyperfaces and cusps among all hyperbolic right-angled polyhedra of the corresponding dimension. This fact is used in the proof of the main result