La conjecture des soufflets  [ The bellows conjecture ]
Séminaire Bourbaki : volume 2002/2003, exposés 909-923, Astérisque, no. 294 (2004), Talk no. 912, p. 77-95

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.

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.

Classification:  52C25,  52B10,  52B45
Keywords: flexible polyhedra, volume, places
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     author = {Schlenker, Jean-Marc},
     title = {La conjecture des soufflets},
     booktitle = {S\'eminaire Bourbaki : volume 2002/2003, expos\'es 909-923},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Association des amis de Nicolas Bourbaki, Soci\'et\'e math\'ematique de France},
     address = {Paris},
     number = {294},
     year = {2004},
     note = {talk:912},
     pages = {77-95},
     zbl = {1078.52014},
     language = {fr},
     url = {http://www.numdam.org/item/SB_2002-2003__45__77_0}
}
Schlenker, Jean-Marc. La conjecture des soufflets, in Séminaire Bourbaki : volume 2002/2003, exposés 909-923, Astérisque, no. 294 (2004), Talk no. 912, pp. 77-95. http://www.numdam.org/item/SB_2002-2003__45__77_0/

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