[Banach] Abstract of a paper by Shlomo Reisner, Carsten Schutt and Elisabeth M. Werner

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