Two new proofs of partial Godbersen's Conjecture

Abstract

Two new proofs are provided, offering two new perspectives on Godbersen's conjecture. One of the proofs utilizes Helly's theorem to provide a concise and elegant proof of the inequality in Godbersen's conjecture. The other proof utilizes the Brunn-Minkowski inequality to provide a completely new proof of the inclusion $-K\subset nK$ for convex bodies $K$ with centroid at the origin, thereby proving Godbersen's conjecture.