The Characteristic Properties of the Minimal Lp-Mean Width

Abstract EN

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, and give the condition for the minimum position of Mp(K).