This is an announcement for the paper "A note on Mahler's conjecture" by Shlomo Reisner, Carsten Schutt and Elisabeth M. Werner.

Abstract: Let $K$ be a convex body in $\mathbb{R}^n$ with Santal'o point at $0$. We show that if $K$ has a point on the boundary with positive generalized Gau{\ss} curvature, then the volume product $|K| |K^\circ|$ is not minimal. This means that a body with minimal volume product has Gau{\ss} curvature equal to $0$ almost everywhere and thus suggests strongly that a minimal body is a polytope.

Archive classification: math.FA

Mathematics Subject Classification: 52A20

Submitted from: elisabeth.werner@case.edu

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

http://front.math.ucdavis.edu/1009.3583

or

http://arXiv.org/abs/1009.3583