Taiwanese Journal of Mathematics

THE MEAN MINKOWSKI MEASURES FOR CONVEX BODIES OF CONSTANT WIDTH

HaiLin Jin and Qi Guo

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Abstract

In this paper, we study the so-called mean Minkowski measures, proposed and studied by Toth in a series of papers, for convex bodies of constant width. We show that, with respect to the mean Minkowski measure, the completions of regular simplices are, as well as for many other measures, the most asymmetric ones among all convex bodies of constant width.

Article information

Source
Taiwanese J. Math., Volume 18, Number 4 (2014), 1283-1291.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706490

Digital Object Identifier
doi:10.11650/tjm.18.2014.4198

Mathematical Reviews number (MathSciNet)
MR3245443

Zentralblatt MATH identifier
1357.52002

Subjects
Primary: 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45] 52A39: Mixed volumes and related topics

Keywords
measure of asymmetry mean Minkowski measure convex body of constant width reuleaux triangle Meissner's bodies completion

Citation

Jin, HaiLin; Guo, Qi. THE MEAN MINKOWSKI MEASURES FOR CONVEX BODIES OF CONSTANT WIDTH. Taiwanese J. Math. 18 (2014), no. 4, 1283--1291. doi:10.11650/tjm.18.2014.4198. https://projecteuclid.org/euclid.twjm/1499706490


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References

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