Relative entropy of cone measures and L p centroid bodies
نویسندگان
چکیده
منابع مشابه
Relative entropy of cone measures and Lp centroid bodies
Let K be a convex body in R. We introduce a new affine invariant, which we call ΩK , that can be found in three different ways: (a) as a limit of normalized Lp-affine surface areas; (b) as the relative entropy of the cone measure of K and the cone measure of K◦; (c) as the limit of the volume difference of K and Lp-centroid bodies. We investigate properties of ΩK and of related new invariant qu...
متن کاملar X iv : 0 90 9 . 43 61 v 1 [ m at h . FA ] 2 4 Se p 20 09 Relative entropy of cone measures and L p centroid bodies ∗
Let K be a convex body in R. 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◦, as the limit of the volume difference of K and Lp-centroid bodies. We investigate properties of ΩK and of related new invariant quantities. In...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2011
ISSN: 0024-6115
DOI: 10.1112/plms/pdr030