منابع مشابه
Euclidean sections of convex bodies
This is a somewhat expanded form of a four hours course given, with small variations, first at the educational workshop Probabilistic methods in Geometry, Bedlewo, Poland, July 6-12, 2008 and a few weeks later at the Summer school on Fourier analytic and probabilistic methods in geometric functional analysis and convexity, Kent, Ohio, August 13-20, 2008. The main part of these notes gives yet a...
متن کاملGaussian Measure of Sections of convex bodies
In this paper we study properties of sections of convex bodies with respect to the Gaussian measure. We develop a formula connecting the Minkowski functional of a convex symmetric body K with the Gaussian measure of its sections. Using this formula we solve an analog of the Busemann-Petty problem for Gaussian measures.
متن کاملAsymptotics of Cross Sections for Convex Bodies
For normed isotropic convex bodies in R n we investigate the behaviour of the (n ? 1)-dimensional volume of intersections with hyperplanes orthogonal to a xed direction, considered as a function of the distance of the hyperplane to the origin. It is a conjecture that for arbitrary normed isotropic convex bodies and random directions this function { with high probability { is close to a Gaussian...
متن کاملExtremal Distances between Sections of Convex Bodies
Let K, D be convex centrally symmetric bodies in R. Let k < n and let dk(K, D) be the smallest Banach–Mazur distance between k-dimensional sections of K and D. Define ∆(k, n) = sup dk(K, D), where the supremum is taken over all n−dimensional convex symmetric bodies K, D. We prove that for any k < n ∆(k, n) ∼log n {√ k if k ≤ n k2 n if k > n , where A ∼log n B means that 1/(C log n) ·A ≤ B ≤ (C ...
متن کاملThe Cross-section Body, Plane Sections of Convex Bodies and Approximation of Convex Bodies, Ii*
We compare the volumes of projections of convex bodies and the volumes of the projections of their sections, and, dually, those of sections of convex bodies and of sections of their circumscribed cylinders. For L ⊂ R a convex body, we take n random segments in L and consider their ‘Minkowski average’ D. For fixed n, the pth moments of V (D) (1 ≤ p < ∞) are minimized, for V (L) fixed, by the ell...
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: Acta Mathematica
سال: 1960
ISSN: 0001-5962
DOI: 10.1007/bf02546358