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.
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页码：177 / 211
页数：35
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