English

Two new proofs of partial Godbersen's Conjecture

Metric Geometry 2024-06-06 v2 Combinatorics

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 KnK-K\subset nK for convex bodies KK with centroid at the origin, thereby proving Godbersen's conjecture.

Keywords

Cite

@article{arxiv.2406.00278,
  title  = {Two new proofs of partial Godbersen's Conjecture},
  author = {Lin Cheng},
  journal= {arXiv preprint arXiv:2406.00278},
  year   = {2024}
}