An intrinsic volume metric for the class of convex bodies in ℝn

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-08-29 DOI:10.1142/S0219199723500062

Florian Besau, Steven Hoehner

引用次数: 2

Abstract

A new intrinsic volume metric is introduced for the class of convex bodies in $\mathbb{R}^n$. As an application, an inequality is proved for the asymptotic best approximation of the Euclidean unit ball by arbitrarily positioned polytopes with a restricted number of vertices under this metric. This result improves the best known estimate, and shows that dropping the restriction that the polytope is contained in the ball or vice versa improves the estimate by at least a factor of dimension. The same phenomenon has already been observed in the special cases of volume, surface area and mean width approximation of the ball.

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一类凸体的内禀体积度规

为$\mathbb｛R｝^n$中的一类凸体引入了一个新的本征体积度量。作为一个应用，证明了在该度量下，任意定位的具有有限顶点数的多面体对欧氏单位球的渐近最佳逼近的一个不等式。这一结果改进了最已知的估计，并表明放弃多面体包含在球中的限制或反之亦然，至少将估计提高了一个维度因子。在球的体积、表面积和平均宽度近似的特殊情况下，也观察到了同样的现象。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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