Quantitative stability in the isodiametric inequality via the\n isoperimetric inequality

2011/04/20 by Francesco Maggi, Maggi, Francesco, Marcello Ponsiglione +3
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Variational Analysis #Point processes and geometric inequalities #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.1104.4074

openalex publication_date 2011/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The isodiametric inequality is derived from the isoperimetric inequality\ntrough a variational principle, establishing that balls maximize the perimeter\namong convex sets with fixed diameter. This principle brings also quantitative\nimprovements to the isodiametric inequality, shown to be sharp by explicit\nnearly optimal sets.\n

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