The Characteristic Properties of the Minimal -Mean Width

Giannopoulos proved that a smooth convex body has minimal mean width position if and only if the measure , supported on , is isotropic. Further, Yuan and Leng extended the minimal mean width to the minimal -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 -mean width of convex bodies and prove the existence and uniqueness of the minimal -mean width in its images. In addition, we establish a characterization of the minimal -mean width, conclude the average with a variation of the minimal -mean width position, and give the condition for the minimum position of .