The bellows conjecture

Jean-Marc Schlenker

Séminaire Bourbaki (2002-2003)

  • Volume: 45, page 77-96
  • ISSN: 0303-1179

Abstract

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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.

How to cite

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Schlenker, Jean-Marc. "La conjecture des soufflets." Séminaire Bourbaki 45 (2002-2003): 77-96. <http://eudml.org/doc/252129>.

@article{Schlenker2002-2003,
abstract = {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.},
author = {Schlenker, Jean-Marc},
journal = {Séminaire Bourbaki},
keywords = {flexible polyhedra; volume; places},
language = {fre},
pages = {77-96},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {La conjecture des soufflets},
url = {http://eudml.org/doc/252129},
volume = {45},
year = {2002-2003},
}

TY - JOUR
AU - Schlenker, Jean-Marc
TI - La conjecture des soufflets
JO - Séminaire Bourbaki
PY - 2002-2003
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 45
SP - 77
EP - 96
AB - 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.
LA - fre
KW - flexible polyhedra; volume; places
UR - http://eudml.org/doc/252129
ER -

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