Abstract
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.
Original language | English (US) |
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Pages (from-to) | 1-16 |
Number of pages | 16 |
Journal | International Mathematics Research Notices |
Volume | 2012 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 2012 |
Bibliographical note
Funding Information:This work was partially supported by an NSF grant, a FRG-NSF grant and a BSF grant (to E.W.).