Moscow Mathematical Journal
Volume 17, Issue 2, April–June 2017 pp. 269–290.
The Bellows Conjecture for Small Flexible Polyhedra in Non-Euclidean Spaces
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.
Authors:
Alexander A. Gaifullin (1)
Author institution:(1) Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina str. 8, Moscow, 119991, Russia
Summary:
Keywords: Flexible polyhedron, the bellows conjecture, simplicial collapse, analytic continuation.
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