论文标题
$ \ mathbb {r}^n $中凸面机构的固有卷度量
An intrinsic volume metric for the class of convex bodies in $\mathbb{R}^n$
论文作者
论文摘要
在$ \ mathbb {r}^n $中引入了一个新的固有卷度量。作为一种应用，通过任意定位的多面体将欧几里得单位球的渐近最佳近似值证明了不等式，并在此度量标准下具有限制数量的顶点。该结果改善了最著名的估计值，并表明删除了polytope包含在球中或反之亦然的限制会使估计值至少提高了一个维度。在特殊的体积，表面积和球的平均宽度近似情况下，已经观察到相同的现象。
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.
