论文标题
地位的等法问题
Isoperimetric problems for zonotopes
论文作者
论文摘要
Shephard（Canad。J.Math。26：302-321，1974）证明了分解定理，用于发挥其体积的简单公式。在本说明中，我们证明了该定理的概括为它们的内在体积产生相似的公式。我们使用此结果来研究给定数量片段产生的地位的几何极差问题。特别是，我们解决了由D或D+1个段产生的D维界定的等等问题，并为相似问题的溶液提供了由足够多个段产生的划分的类似问题的解决方案。此外，我们将结果应用于单位球体上的\ ell_1 $极化问题，以及2021年Brazitikos和McIntyre猜想的矢量值Maclaurin不等式。
Shephard (Canad. J. Math. 26: 302-321, 1974) proved a decomposition theorem for zonotopes yielding a simple formula for their volume. In this note we prove a generalization of this theorem yielding similar formulas for their intrinsic volumes. We use this result to investigate geometric extremum problems for zonotopes generated by a given number of segments. In particular, we solve isoperimetric problems for d-dimensional zonotopes generated by d or d+1 segments, and give asymptotic estimates for the solutions of similar problems for zonotopes generated by sufficiently many segments. In addition, we present applications of our results to the \ell_1$ polarization problem on the unit sphere and to a vector-valued Maclaurin inequality conjectured by Brazitikos and McIntyre in 2021.
