The Characteristic Properties of the Minimal Lp-Mean Width

Giannopoulos proved that a smooth convex body k has minimal mean width position if and only if the measure hk(u)σ(du),supported on sn-1,is isotropic.further,yuan and leng extended the minimal mean width to the minimal lp-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 lp-mean width of convex bodies and prove the existence and uniqueness of the minimal lp-mean width in its sl(n) images.in addition,we establish a characterization of the minimal lp-mean width,conclude the average mp(k) with a variation of the minimal lp-mean width position,andgive the condition for the minimum position of mp(k). © 2017 tongyi ma.