Optimal divisions of a convex body

2023/11/23 by Antonio Cañete, Cañete, Antonio, Isabel Fernández +3
Mathematics · #52A20 #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2311.13882

openalex publication_date 2023/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a convex body C in ℝ^d and a division of C into convex subsets C₁,…,C_n, we can consider max\F(C₁),…, F(C_n)\ (respectively, min\F(C₁),…, F(C_n)\), where F represents one of these classical geometric magnitudes: the diameter, the minimal width, or the inradius. In this work we study the divisions of C minimizing (respectively, maximizing) the previous value, as well as other related questions.

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