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 , , is introduced. Then we study the minimization problems of the form 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 are obtained, a stability result for -centroid bodies is established, and some new applications for the minimal Orlicz mean width position are provided.
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).