Circumscribed Simplices of Minimal Mean Width

Abstract. It is proved that the minimal mean width of all simplices cir-cumscribed about a convex body of given mean width attains its maximum precisely if the body is a ball. An analogous result holds for circumscribed parallelepipeds, with balls replaced by bodies of constant width. MSC 2000: 52A20, 52A40 1. Introduction and main result. For a convex body K (a compact convex set with interior points) in Euclidean space Rn (n ¸ 2), we denote by M(K) its mean width and by TK a simplex of minimal mean width circumscribed about K. Let T n be a regular simplex circumscribed about the unit ball Bn of Rn. In this note, we prov