The Characteristic Properties of the Minimal Lp-Mean Width. (20th June 2017)

• Record Type: Journal Article
• Authors: Ma, Tongyi
• Other Names: Granero Antonio S. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2017(2017)
• Publication Date: 2017-06-20
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2017/2943073
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Giannopoulos proved that a smooth convex body K has minimal mean width position if and only if the measure h K ( u ) σ ( d u ), supported on S n - 1, is isotropic. Further, Yuan and Leng extended the minimal mean width to the minimal L p -mean width and characterized the minimal position of convex bodies in terms of isotropicity of a suitable measure. In this paper, we study the minimal L p -mean width of convex bodies and prove the existence and uniqueness of the minimal L p -mean width in its S L ( n ) images. In addition, we establish a characterization of the minimal L p -mean width, conclude the average M p ( K ) with a variation of the minimal L p -mean width position, and give the condition for the minimum position of M p ( K ) .