Minimal area \(n\)-simplex circumscribing a strictly convex body in \({\mathbb{R}}^n\) (Q2474144)

Let \(S\) be a minimal area \(n\)-simplex circumscribed about a strictly convex body \(C \subset \mathbb{R}^n\) with nonempty interior. Let \(J\) be the homothety with ratio \(1/(1-n)\) centered at the centroid of a face of \(S\). The authors prove that the tangency points of \(C\) with \(S\) are exactly the tangency points of the spheres inscribed in the images \(J(S)\) with \(S\). This generalizes analogous results for \(n=2\) by \textit{M. Levi} [Am. Math. Mon. 109, No. 10, 890--899 (2002; Zbl 1037.52004)] and for \(n=3\) by the authors [J. Convex Anal. 14, No. 1, 27--33 (2007; Zbl 1141.52003)].