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-dimensional Lobachevsky spaces Λ2m+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 Sn or Λn, n ≥ 3, with sufficiently small edge lengths.
|Number of pages||22|
|Journal||Moscow Mathematical Journal|
|Publication status||Published - 2017|
- Analytic continuation
- Flexible polyhedron
- Simplicial collapse
- The bellows conjecture