On volumes of hyperbolic right-angled polyhedra

Abstract

In this paper we obtain new upper bounds on volumes of right-angled polyhedra in hyperbolic space ${\mathbb{H}}^3$ in three different cases: for ideal polyhedra with all vertices on the ideal hyperbolic boundary, for compact polytopes with only finite (or usual) vertices, and for finite volume polyhedra with vertices of both types.

15 pages, 6 figures