Relative entropy of cone measures and Lp centroid bodies Academic Article uri icon


  • Let K be a convex body in ℝ n. We introduce a new affine invariant, which we call Ω K, that can be found in three different ways: as a limit of normalized L p-affine surface areas;as the relative entropy of the cone measure of K and the cone measure of K°;as the limit of the volume difference of K ̊ and L p-centroid bodies. We investigate properties of Ω K and of related new invariant quantities. In particular, we show new affine isoperimetric inequalities and we show an 'information inequality' for convex bodies. © 2011 London Mathematical Society.

author list (cited authors)

  • Paouris, G., & Werner, E. M.

citation count

  • 60

publication date

  • August 2011