THE BELLOWS CONJECTURE FOR SMALL FLEXIBLE POLYHEDRA IN NON-EUCLIDEAN SPACES

被引：3

作者：

Gaifullin, Alexander A. ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Gubkina Str 8, Moscow 119991, Russia

来源：

MOSCOW MATHEMATICAL JOURNAL | 2017年 / 17卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

Flexible polyhedron; the bellows conjecture; simplicial collapse; analytic continuation; DIMENSIONS;

D O I：

10.17323/1609-4514-2017-17-2-269-290

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The bellows conjecture claims that the volume of any flexible polyhedron of dimension 3 or higher is constant during the flexion. The bellows conjecture was proved for flexible polyhedra in Euclidean spaces R-n, n >= 3, and for bounded flexible polyhedra in odd-dimensional Lobachevsky spaces A(2m+1), m >= 1. Counterexamples to the bellows conjecture are known in all open hemispheres S-n, n >= 3. The aim of this paper is to prove that, nonetheless, the bellows conjecture is true for all flexible polyhedra in either S-n or A(n), n >= 3, with sufficiently small edge lengths.

引用

页码：269 / 290

页数：22

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