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Two new proofs of partial Godbersen's Conjecture
- Publication Year :
- 2024
-
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.
- Subjects :
- Mathematics - Metric Geometry
Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.00278
- Document Type :
- Working Paper