On Godbersen’s conjecture

Shiri Artstein-Avidan*, Keshet Einhorn, Dan I. Florentin, Yaron Ostrover

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We provide a natural generalization of a geometric conjecture of Fáry and Rédei regarding the volume of the convex hull of K ⊂ Rn, and its negative image -K. We show that it implies Godbersen’s conjecture regarding the mixed volumes of the convex bodies K and -K. We then use the same type of reasoning to produce the currently best known upper bound for the mixed volumes V(K[j], -K[n - j]), which is not far from Godbersen’s conjectured bound. To this end we prove a certain functional inequality generalizing Colesanti’s difference function inequality.

Original languageEnglish
Pages (from-to)337-350
Number of pages14
JournalGeometriae Dedicata
Volume178
Issue number1
DOIs
StatePublished - 24 Oct 2015

Funding

FundersFunder number
European Research Council305629, 1057/10, SSGHD-268274
Israel Science Foundation247/11

    Keywords

    • Convex body
    • Convex hull
    • Difference body
    • Godbersen’s conjecture
    • Mixed volume
    • Rogers–Shephard inequality

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