On the volume of the convex hull of d 1 segments in Rd

摘要

Let d ≥ 2, m ≥ d, and u_i,..., u_mbe non-zero vectors linearly span-ning Rd. The note is devoted to the problem of minimizing the volume of the polytopes P := conv(I_1 U UI_m),where, forj =1,, m, I_jis a translate of conv{o, u_j}. Thesolution of this problem for the case m = d was previously known. For the case m = d+ 1the minimal volume is evaluated and the class of minimizing polytopes P is studied.