2021/12/27 by René Brandenberg, Brandenberg, René, Katherina von Dichter +3 · 1 citation
Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Mathematical Inequalities and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2112.13590
openalex publication_date 2021/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper deals with four symmetrizations of a convex set C: the intersection, the harmonic and the arithmetic mean, and the convex hull of C and -C. A well-known result of Firey shows that those means build up a subset-chain in the given order. On the one hand, we determine the dilatation factors, depending on the asymmetry of C, to reverse the containments between any of those symmetrizations. On the other hand, we tighten the relations proven by Firey and show a stability result concerning those factors near the simplex.