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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 9
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Research Article

The minimal Orlicz mean width of convex bodies

Pages 3316-3346 | Received 24 Jan 2019, Accepted 19 Jun 2020, Published online: 17 Nov 2020
 

ABSTRACT

In this paper, we generalize the minimal p-mean width of convex bodies (including the classic minimal mean width) to the Orlicz Brunn–Minkowski–Firey theory. The concept of Orlicz mean width of a convex body K in Rn, wϕ(K), is introduced. Then we study the minimization problems of the form min{wϕ(TK):TSL(n)} and show that bodies which appear as solutions of such problems satisfy isotropic conditions of a suitable measure. Finally, the characteristics of the condition for the minimum Mϕ(K)Mϕ(K) are obtained, a stability result for Lp-centroid bodies is established, and some new applications for the minimal Orlicz mean width position are provided.

2010 Mathematics Subject Classifications:

Acknowledgements

Author would like to thank Dr. J. Li and Dr. Y. B. Feng for some helpful help.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant No. 11561020).

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