Bisections of centrally symmetric planar convex bodies minimizing the\n maximum relative diameter

2018/03/01 by Antonio Cañete, Cañete, Antonio, Salvador Segura Gomis +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #Prion Diseases and Protein Misfolding

paper · pdf · doi:10.48550/arxiv.1803.00321

openalex publication_date 2018/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the bisections of a centrally symmetric planar convex\nbody which minimize the maximum relative diameter functional. We give necessary\nand sufficient conditions for being a minimizing bisection, as well as\nanalyzing the behavior of the so-called standard bisection.\n

Related

• Subdivisions of rotationally symmetric planar convex bodies minimizing the maximum relative diameter
• The maximum relative diameter for multi-rotationally symmetric planar\n convex bodies
• Optimal divisions of a convex body
• On the isodiametric and isominwidth inequalities for planar bisections
• Narrowing the gaps of the missing Blaschke-Santaló diagrams