Key points are not available for this paper at this time.
It is shown that if C is an n-dimensional convex body then there is an affine image C ˜ of C for which |∂ C ˜ |/| C ˜ (n−1)/n is no larger than the corresponding expression for a regular n-dimensional ‘tetrahedron’. It is also shown that among n-dimensional subspaces of Lp (for eachp∈1,∞), l p n has maximal volume ratio.
Keith Ball (Tue,) studied this question.