Mahler's conjecture and curvature

Shlomo Reisner, Carsten Schütt, Elisabeth M. Werner

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)1-16
Number of pages16
JournalInternational Mathematics Research Notices
Issue number1
StatePublished - 1 Jan 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.).

ASJC Scopus subject areas

  • General Mathematics


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