The maximum relative diameter for multi-rotationally symmetric planar\n convex bodies

2015/11/25 by Antonio Cañete, Cañete, Antonio
Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1511.08009

openalex publication_date 2015/11/25 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this work we study the maximum relative diameter functional d_M in the\nclass of multi-rotationally symmetric planar convex bodies. A given set C of\nthis class is k-rotationally symmetric for\nk\∈ k₁,\…,k_n \⊂ nn, and so it is natural to consider the\nstandard k_i-partition P_ki associated to C (which is a minimizing\nk_i-partition for d_M when k_i\≥3) and the corresponding value\nd_M(P_ki). We establish the relation among these values, characterizing\nthe particular sets for which all these values coincide.\n

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