Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra

被引：5

作者：

Atkinson, Christopher K. ^{[1
]}

机构：

[1] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

来源：

GEOMETRIAE DEDICATA | 2011年 / 153卷 / 01期

关键词：

Hyperbolic geometry; Volume; Polyhedron; 3-ORBIFOLDS; TETRAHEDRA; 3-SPACE; FORMULA;

D O I：

10.1007/s10711-010-9563-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorithm that detects the geometric decomposition of good 3-orbifolds with planar singular locus and underlying manifold S (3). The volume bounds follow from techniques related to the proof of Thurston's Orbifold Theorem, Schlafli's formula, and previous results of the author giving volume bounds for right-angled hyperbolic polyhedra.

引用

页码：177 / 211

页数：35

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