This is an announcement for the paper "Minimal volume product near Hanner polytopes" by Jaegil Kim.

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.

Archive classification: math.FA math.MG

Mathematics Subject Classification: 52A20, 52A40, 52B11

Submitted from: jkim@math.kent.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1212.2544

or

http://arXiv.org/abs/1212.2544