Relative entropy of cone measures and <i>L</i> <sub> <i>p</i> </sub> centroid bodies
Relative entropy of cone measures and <i>L</i> <sub> <i>p</i> </sub> centroid bodies
Let K be a convex body in ℝn. We introduce a new affine invariant, which we call ΩK, that can be found in three different ways: as a limit of normalized Lp-affine surface areas; as the relative entropy of the cone measure of K and the cone measure of K°; …