منابع مشابه
Orlicz Centroid Bodies
The sharp affine isoperimetric inequality that bounds the volume of the centroid body of a star body (from below) by the volume of the star body itself is the Busemann-Petty centroid inequality. A decade ago, the Lp analogue of the classical BusemannPetty centroid inequality was proved. Here, the definition of the centroid body is extended to an Orlicz centroid body of a star body, and the corr...
متن کاملOrlicz Projection Bodies
As Schneider [50] observes, the classical Brunn-Minkowski theory had its origin at the turn of the 19th into the 20th century, when Minkowski joined a method of combining convex bodies (which became known as Minkowski addition) with that of ordinary volume. One of the core concepts that Minkowski introduced within the Brunn-Minkowski theory is that of projection body (precise definitions to fol...
متن کاملCentroid Bodies and Comparison of Volumes
For −1 < p < 1 we introduce the concept of a polar pcentroid body ΓpK of a star body K. We consider the question of whether ΓpK ⊂ ΓpL implies vol(L) ≤ vol(K). Our results extend the studies by Lutwak in the case p = 1 and Grinberg, Zhang in the case p > 1.
متن کاملRelative 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 کاملA stability result for mean width of L p - centroid bodies
We give a different proof of a recent result of Klartag [12] concerning the concentration of the volume of a convex body within a thin Euclidean shell and proving a conjecture of Anttila, Ball and Perissinaki [1]. It is based on the study of the Lp-centroid bodies. We prove an almost isometric reverse Hölder inequality for their mean width and a refined form of a stability result.
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2010
ISSN: 0022-040X
DOI: 10.4310/jdg/1274707317