柯西表面积公式的矢量类似公式

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-01-29 DOI:10.1007/s00013-023-01962-y

Daniel Hug, Rolf Schneider

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引用次数: 0

摘要

考基表面积公式指出，对于 n 维欧几里得空间中的凸体 K，K 向超平面的正交投影的 \((n-1)\) 维体积的平均值是 K 表面积的常数倍。这就需要在凸体上引入一个新的向量值估值。

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Vectorial analogues of Cauchy’s surface area formula

Cauchy’s surface area formula says that for a convex body K in n-dimensional Euclidean space, the mean value of the \((n-1)\)-dimensional volumes of the orthogonal projections of K to hyperplanes is a constant multiple of the surface area of K. We prove an analogous formula, with the volumes of the projections replaced by their moment vectors. This requires to introduce a new vector-valued valuation on convex bodies.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.