Mahler's conjecture for some hyperplane sections

Abstract

We use symplectic techniques to obtain partial results on Mahler's conjecture about the product of the volume of a convex body and the volume of its polar. We confirm the conjecture for hyperplane sections or projections of ${\ell }_p$-balls or the Hanner polytopes.

References in corpus (4)

• Symmetric Mahler's conjecture for the volume product in the three dimensional case
• When symplectic topology meets Banach space geometry
• Lower and upper bounds for the waists of different spaces
• Estimating symplectic capacities from lengths of closed curves on the unit spheres

Cited by in corpus (2)

• Stochastic reverse isoperimetric inequalities in the plane
• Symplectic polarity and Mahler's conjecture