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

共 3 条

[1] Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra
Christopher K. Atkinson
Geometriae Dedicata, 2011, 153 : 177 - 211
[2] TWO-SIDED ASYMPTOTIC BOUNDS FOR THE COMPLEXITY OF SOME CLOSED HYPERBOLIC THREE-MANIFOLDS
Matveev, Sergei
Petronio, Carlo
Vesnin, Andrei
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2009, 86 (02) : 205 - 219
[3] TWO-SIDED BOUNDS FOR THE COMPLEXITY OF CYCLIC BRANCHED COVERINGS OF TWO-BRIDGE LINKS
Petronio, Carlo
Vesnin, Andrei
OSAKA JOURNAL OF MATHEMATICS, 2009, 46 (04) : 1077 - 1095

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