Let K be a convex body in ℝn with Santaló point at 0. We show that if K has a point on the boundary with positive generalized Gauß curvature, then the volume product |K||K°|is not minimal. This means that a body with minimal volume product has a Gauß curvature equal to 0 almost everywhere and thus suggests strongly that a minimal body is a polytope.
Bibliographical noteFunding Information:
This work was partially supported by an NSF grant, a FRG-NSF grant and a BSF grant (to E.W.).
ASJC Scopus subject areas
- Mathematics (all)