Volume extremals of general L_p-centroid bodies
نویسندگان
چکیده
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 کاملApproximating the Volume of General Pfaffian Bodies
We introduce a new powerful method of approximating the volume (and integrals) for a vast number of geometric body classes defined by boolean combinations of Pfaffian conditions. The method depends on the VC Dimension of the underlying classes of bodies. The resulting approximation algorithms are quite different in spirit from the other up to now known methods, and give randomized solutions eve...
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 کاملCharacterizations of extremals for some functionals on convex bodies
We investigate equality cases in inequalities for Sylvester-type functionals. Namely, it was proven by Campi, Colesanti and Gronchi that the quantity ∫ x0∈K ... ∫ xn∈K [V (conv{x0, ..., xn})]dx0...dxn , n ≥ d, p ≥ 1 is maximized by triangles among all planar convex bodies K (parallelograms in the symmetric case). We show that these are the only maximizers, a fact proven by Giannopoulos for p = ...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2017
ISSN: 1846-579X
DOI: 10.7153/jmi-11-19