Minimal volume product near Hanner polytopes
Functional Analysis
2016-11-26 v1 Metric Geometry
Abstract
Mahler's conjecture asks whether the cube is a minimizer for the volume product of a body and its polar in the class of symmetric convex bodies in a fixed dimension. It is known that every Hanner polytope has the same volume product as the cube or the cross-polytope. In this paper we prove that every Hanner polytope is a strict local minimizer for the volume product in the class of symmetric convex bodies endowed with the Banach-Mazur distance.
Keywords
Cite
@article{arxiv.1212.2544,
title = {Minimal volume product near Hanner polytopes},
author = {Jaegil Kim},
journal= {arXiv preprint arXiv:1212.2544},
year = {2016}
}