La conjecture des soufflets

Schlenker, Jean-Marc

Séminaire Bourbaki : volume 2002/2003, exposés 909-923, Astérisque, no. 294 (2004), Exposé no. 912, pp. 77-95.

On sait depuis les travaux de Bricard et de Connelly qu'il existe dans l'espace euclidien des polyèdres (non convexes) qui sont flexibles : on peut les déformer continûment sans changer la forme de leurs faces. La conjecture des soufflets affirme que le volume interieur de ces polyèdres est constant au cours de la déformation. Elle a été démontrée récemment par I. Sabitov, qui a pour cela utilisé des outils algébriques inattendus dans ce contexte.

Bricard and Connelly showed that there are (non-convex) polyhedra in euclidean space which are flexible: one can deform them continuously without changing the shape of their faces. The Bellows Conjecture states that the volume bounded by those polyhedra remains constant during the flex. It was proved recently by I. Sabitov, using algebraic tools which were unexpected in this context.

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