On the isotropic constant of non-symmetric convex bodies
The isotropic constant \(L_K\) is an affine invariant of a convex body \(K\). It is well-known that for symmetric bodies in \(\mathbb{R}^n\) the invariant \(L_K\) has an upper bound \(\sqrt n\) (up to a constant factor). Here it is shown that this is also true in the general case. This is achieved by introducing the isotropic constants for finite point sets and proving such an inequality for this case.
scientific article; zbMATH DE number 1011394