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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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00793781
Contributor : Matthieu Fradelizi <>
Submitted on : Friday, February 22, 2013 - 11:56:07 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
Long-term archiving on: : Sunday, April 2, 2017 - 4:36:31 AM

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  • HAL Id : hal-00793781, version 1

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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. ⟨hal-00793781⟩

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