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Volume estimates for right-angled hyperbolic polyhedra (2010.11147v1)

Published 21 Oct 2020 in math.GT

Abstract: By Andreev theorem acute-angled polyhedra of finite volume in a hyperbolic space $\mathbb H{3}$ are uniquely determined by combinatorics of their 1-skeletons and dihedral angles. For a class of compact right-angled polyhedra and a class of ideal right-angled polyhedra estimates of volumes in terms of the number of vertices were obtained by Atkinson in 2009. In the present paper upper estimates for both classes are improved.

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