Mahler's conjecture and curvature

Shlomo Reisner, Carsten Schütt, Elisabeth M. Werner

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

Let K be a convex body in ℝ n 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 languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalInternational Mathematics Research Notices
Volume2012
Issue number1
DOIs
StatePublished - Jan 23 2012

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