The minimal Orlicz mean width of convex bodies. Issue 9 (13th June 2022)

• Record Type: Journal Article
• Authors: Ma, Tongyi
• Is Part Of: Applicable analysis. Volume 101:Issue 9(2022)
• Page Start: 3316
• Page End: 3346
• Publication Date: 2022-06-13
• Subjects: Convex body -- isotropic measure -- p-mean width -- Orlicz mean width; 52A30 -- 52A40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1849627
• Languages: English
• ISSNs: 0003-6811

Abstract

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 R n, w ϕ ( K ), is introduced. Then we study the minimization problems of the form min { w ϕ ( T K ) : T ∈ S L ( 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 M ϕ ( K ) M ϕ ∗ ( K ) are obtained, a stability result for L p -centroid bodies is established, and some new applications for the minimal Orlicz mean width position are provided.