Previous issue ·  Next issue ·  Recently posted articles ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

Moscow Mathematical Journal

Volume 17, Issue 2, April–June 2017  pp. 269–290.

The Bellows Conjecture for Small Flexible Polyhedra in Non-Euclidean Spaces

Authors:  Alexander A. Gaifullin (1)
Author institution:(1) Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, Moscow, 119991, Russia


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 ℝn, n ≥ 3, and for bounded flexible polyhedra in odd-dimensionala Lobachevsky spaces Λ2m+1, m ≥ 1. Counterexamples to the bellows conjecture are known in all open hemispheres 𝕊n+, n ≥ 3. The aim of this paper is to prove that, nonetheless, the bellows conjecture is true for all flexible polyhedra in either 𝕊n or Λn, n ≥ 3, with sufficiently small edge lengths.

2010 Math. Subj. Class. Primary: 52C25, Secondary: 51M25, 05E45, 32D99.

Keywords: Flexible polyhedron, the bellows conjecture, simplicial collapse, analytic continuation.

Contents   Full-Text PDF