Volume estimates for right-angled hyperbolic polyhedra

2020/10/21 by Egorov, A., Vesnin, A. · 1 citation
#52B10 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2010.11147

Abstract

By Andreev theorem acute-angled polyhedra of finite volume in a hyperbolic space \mathbb H³ 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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