Skip to Main content Skip to Navigation
Journal articles

The volume product of convex bodies with many hyperplane symmetries

Abstract : Mahler's conjecture predicts a sharp lower bound on the volume of the polar of a convex body in terms of its volume. We confirm the conjecture for convex bodies with many hyperplane symmetries in the following sense: their hyperplanes of symmetries have a one-point intersection. Moreover, we obtain improved sharp lower bounds for classes of convex bodies which are invariant by certain reflection groups, namely direct products of the isometry groups of regular polytopes.
Document type :
Journal articles
Complete list of metadata

Cited literature [22 references]  Display  Hide  Download
Contributor : Matthieu Fradelizi Connect in order to contact the contributor
Submitted on : Friday, February 22, 2013 - 11:56:07 PM
Last modification on : Monday, July 4, 2022 - 9:20:37 AM
Long-term archiving on: : Sunday, April 2, 2017 - 4:36:31 AM


Files produced by the author(s)



Franck Barthe, Matthieu Fradelizi. The volume product of convex bodies with many hyperplane symmetries. American Journal of Mathematics, Johns Hopkins University Press, 2013, 135 (2), pp.1-37. ⟨10.1353/ajm.2013.0018⟩. ⟨hal-00793781⟩



Record views


Files downloads