Relative entropy of cone measures and L-p centroid bodies Academic Article uri icon

abstract

  • Let K be a convex body in n. We introduce a new affine invariant, which we call 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 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.

published proceedings

  • PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY

author list (cited authors)

  • Paouris, G., & Werner, E. M.

citation count

  • 77

complete list of authors

  • Paouris, Grigoris||Werner, Elisabeth M

publication date

  • February 2012

publisher