A note on Mahler's conjecture

Details A note on Mahler's conjecture A note on Mahler's conjecture

2010-09-18

arxiv.org/abs/1009.3583v1

Mathematics

Functional Analysis

Scientific paper

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.

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