On Godbersen’s conjecture

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

doi:10.1007/s10711-015-0060-1

On Godbersen’s conjecture

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

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

14 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 language	English
Pages (from-to)	337-350
Number of pages	14
Journal	Geometriae Dedicata
Volume	178
Issue number	1
DOIs	https://doi.org/10.1007/s10711-015-0060-1
State	Published - 24 Oct 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.

Keywords

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

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10.1007/s10711-015-0060-1

Cite this

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KW - Convex hull

KW - Difference body

KW - Godbersen’s conjecture

KW - Mixed volume

KW - Rogers–Shephard inequality

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On Godbersen’s conjecture

Abstract

Bibliographical note

Keywords

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