Convex bodies with few faces

Keith Ball, Alain Pajor

It is proved that if $u_1,\dots ,u_n$ are vectors in ${\mathbb{R}}^k,k\le n,1\le p<\infty$ and $$r=(\frac{1}{k}\sum _1^n|u_i{|}^p{)}^{\frac{1}{p}}$$ then the volume of the symmetric…