Two new proofs of partial Godbersen's Conjecture

Lin Cheng

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arXiv · 2406.00278

Two new proofs of partial Godbersen's Conjecture

Lin Cheng

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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.

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Lin Cheng. 2024-06-01. Two new proofs of partial Godbersen's Conjecture. https://arxiv.org/abs/2406.00278

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