DOI: 10.4213/sm9740e ISSN:
On volumes of hyperbolic right-angled polyhedra
Stepan Andreevich Alexandrov, Nikolay Vladimirovich Bogachev, Andrei Yurievich Vesnin, Andrei Aleksandrovich Egorov- Algebra and Number Theory
New upper bounds for the volumes of right-angled polyhedra in hyperbolic space $\mathbb{H}^3$ are obtained in the following three cases: for ideal polyhedra with all vertices on the ideal hyperbolic boundary; for compact polyhedra with only finite vertices; and for finite-volume polyhedra with vertices of both types. Bibliography: 23 titles.