2023/03/15 by Antal Joós, Zsolt Lángi · 1 voice
Mathematics · #Analytic and geometric function theory #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · doi:10.1112/mtk.12191
openalex publication_date 2023/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
Abstract Shephard (Canad. J. Math. 26 (1974), 302–321) proved a decomposition theorem for zonotopes yielding a simple formula for their volume. In this note, we prove a generalization of this theorem yielding similar formulae for their intrinsic volumes. We use this result to investigate geometric extremum problems for zonotopes generated by a given number of segments. In particular, we solve isoperimetric problems for d ‐dimensional zonotopes generated by d or segments, and give asymptotic estimates for the solutions of similar problems for zonotopes generated by sufficiently many segments. In addition, we present applications of our results to the ℓ 1 polarization problem on the unit sphere and to a vector‐valued Maclaurin inequality conjectured by Brazitikos and McIntyre in 2021.