On the approximation of a convex body by its radial mean bodies

Volume 9, Issue 5, pp 2846--2856 http://dx.doi.org/10.22436/jnsa.009.05.79

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Authors

Lvzhou Zheng - School of Mathematics and Statistics, Hubei Normal University, 435002 Huangshi, P. R. China.

Abstract

In this paper, we consider the approximation problem on the volume of a convex body \(K\) in \(\mathbb{R}^n\) by those of its radial mean bodies \(R_pK\): Specifically, we establish the identity \[\lim_{p\rightarrow \infty}\frac{P}{\log P}(1-2^{-n}\frac{|R_P(K)|}{|K|})=\frac{n(n+1)}{2};\] when K is an ellipsoid in \(\mathbb{R}^n\).

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Keywords

• Convex body
• radial mean body
• difference body
• restricted chord projection function.

MSC

•  53A40
•  41A25

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