直角双曲多面体的体积估计

arXiv: Geometric Topology Pub Date : 2020-10-21 DOI:10.13137/2464-8728/30958

A. Egorov, A. Vesnin

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引用次数: 4

摘要

根据Andreev定理，双曲空间中有限体积的锐角多面体$\mathbb H^{3}$是由它们的1-骨架和二面角的组合唯一确定的。对于一类紧致直角多面体和一类理想直角多面体，Atkinson(2009)给出了基于顶点数的体积估计。本文改进了这两类的上估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Volume estimates for right-angled hyperbolic polyhedra

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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arXiv: Geometric Topology

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