2023/12/03 by Hermann König, König, Hermann
Computer Science · Mathematics · #52A38 #Computational Geometry and Mesh Generation #FOS: Mathematics #Functional Analysis (math.FA) #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2312.01321
openalex publication_date 2023/12/03 · openalex created_date 2023/12/06 · openalex updated_date 2026/07/28
We determine the maximal non-central hyperplane sections of the n-dimensional l1-ball if the fixed distance of the hyperplane to the origin is between 1 / √ 3 and 1 / √ 2. This adds to a result of Liu and Tkocz who considered the distance range between 1 / √ 2 and 1. For n > 3, the maximal sections are parallel to the (n-1)-dimensional coordinate planes. We also study non-central sections of the complex l12- and l_∞2-balls, where the formulas are more complicated than in the real case. Also, the extrema are partially different than in the real case.