2023/08/19 by Imre Bárány, Barany, Imre
Computer Science · Mathematics · #52A35 #Advanced Topology and Set Theory #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Variational Analysis #Point processes and geometric inequalities
paper · doi:10.48550/arxiv.2308.10106
openalex publication_date 2023/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assume that k ≤ d is a positive integer and \C is a finite collection of convex bodies in \Rd. We prove a Helly type theorem: If for every subfamily \C^*⊂ \C of size at most max \d+1,2(d-k+1)\ the set \bigcap \C^* contains a k-dimensional cone, then so does \bigcap \C. One ingredient in the proof is another Helly type theorem about the dimension of lineality spaces of convex cones.