Two new proofs of partial Godbersen's Conjecture

2024/06/01 by Cheng Lin, Cheng, Lin
Mathematics · #Algebraic and Geometric Analysis #Combinatorics (math.CO) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2406.00278

openalex publication_date 2024/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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⊂ nK for convex bodies K with centroid at the origin, thereby proving Godbersen's conjecture.

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