منابع مشابه
The L-busemann-petty Centroid Inequality
The ratio between the volume of the p-centroid body of a convex body K in Rn and the volume of K attains its minimum value if and only if K is an origin symmetric ellipsoid. This result, the Lp-Busemann-Petty centroid inequality, was recently proved by Lutwak, Yang and Zhang. In this paper we show that all the intrinsic volumes of the p-centroid body of K are convex functions of a time-like par...
متن کاملOn the Reverse L-busemann-petty Centroid Inequality
The volume of the Lp-centroid body of a convex body K ⊂ Rd is a convex function of a time-like parameter when each chord of K parallel to a fixed direction moves with constant speed. This fact is used to study extrema of some affine invariant functionals involving the volume of the Lp-centroid body and related to classical open problems like the slicing problem. Some variants of the Lp-Busemann...
متن کاملAn isoperimetric inequality on the lp balls
The normalised volume measure on the lp unit ball (1 ≤ p ≤ 2) satisfies the following isoperimetric inequality: the boundary measure of a set of measure a is at least cnã log(1/ã), where ã = min(a, 1− a). Résumé Nous prouvons une inégalité isopérimétrique pour la mesure uniforme Vp,n sur la boule unité de l n p (1 ≤ p ≤ 2). Si Vp,n(A) = a, alors V + p,n(A) ≥ cn ã log 1/ã, où V + p,n est la mesu...
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 کاملTHE Lp VERSION OF NEWMAN’S INEQUALITY FOR LACUNARY POLYNOMIALS
The principal result of this paper is the establishment of the essentially sharp Markov-type inequality ‖xP (x)‖Lp[0,1] ≤ 1/p+ 12 n ∑ j=0 (λj + 1/p) ‖P‖Lp[0,1] for every P ∈ span{xλ0 , xλ1 , . . . , xλn} with distinct real exponents λj greater than −1/p and for every p ∈ [1,∞]. A remarkable corollary of the above is the Nikolskii-type inequality ‖yP (y)‖L∞ [0,1] ≤ 13 n ∑ j=0 (λj + 1...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2002
ISSN: 0001-8708
DOI: 10.1006/aima.2001.2036