@article{c95448ec1def449287150672d8459686,
title = "On Godbersen{\textquoteright}s conjecture",
abstract = "We provide a natural generalization of a geometric conjecture of F{\'a}ry and R{\'e}dei regarding the volume of the convex hull of K ⊂ Rn, and its negative image -K. We show that it implies Godbersen{\textquoteright}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{\textquoteright}s conjectured bound. To this end we prove a certain functional inequality generalizing Colesanti{\textquoteright}s difference function inequality.",
keywords = "Convex body, Convex hull, Difference body, Godbersen{\textquoteright}s conjecture, Mixed volume, Rogers–Shephard inequality",
author = "Shiri Artstein-Avidan and Keshet Einhorn and Florentin, {Dan I.} and Yaron Ostrover",
note = "Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media Dordrecht.",
year = "2015",
month = oct,
day = "24",
doi = "10.1007/s10711-015-0060-1",
language = "אנגלית",
volume = "178",
pages = "337--350",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer Netherlands",
number = "1",
}