SLICING lp-BALLS RELOADED: STABILITY, PLANAR SECTIONS IN l1

• 成果类型: Article
• 署名作者: Chasapsis, Giorgos; Nayar, Piotr; Tkocz, Tomasz
• 署名单位: Carnegie Mellon University; University of Warsaw
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1584
• 发表日期: 2022
• 页码: 2344-2372
• 关键词: busemann-petty problem; intersection bodies; unit ball; projections; volume; INEQUALITY; constants; geometry; SPACES; bounds

摘要

We show that the two-dimensional minimum-volume central section of the n-dimensional cross-polytope is attained by the regular 2n-gon. We estab-lish stability-type results for hyperplane sections of l(p)-balls in all the cases where the extremisers are known. Our methods are mainly probabilistic, ex-ploring connections between negative moments of projections of random vec-tors uniformly distributed on convex bodies and volume of their sections.