منابع مشابه
Optimal roughening of convex bodies
A body moves in a rarefied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface, and do not interact with each other. We consider a generalization of Newton’s minimal resistance problem: given two bounded convex bodies C1 and C2 such that C1 ⊂ C2 ⊂ R and ∂C1 ∩∂C2 = ∅, minimize the resistance in the class of connected bodies B su...
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It is proved that if C is a convex body in R" then C has an affine image C (of nonzero volume) so that if P is any 1-codimensional orthogonal projection, \PC\>\C\{tt~l)/n. It is also shown that there is a pathological body, K , all of whose orthogonal projections have volume about \fh~ times as large as |Ä"| . 0. Introduction The problems discussed in this paper concern the areas of shadows (or...
متن کاملReductibility of Convex Bodies
Introduction Let C be a convex bounded body in the n-dimensional Euclidean space E, and let B be its boundary. We use Busemann's notations: E(a,b) for the segment {(1 — p)a + pb: 0 < p ^ 1} from a to b, and S(z, p) for the sphere {x: \\z — x\\ = p). We now recall the definition of Hammer's associated bodies C(r). Let Cb(r) be the set obtained from C by a similitude transformation with a ratio r...
متن کاملEssentially-Euclidean convex bodies
In this note we introduce a notion of essentially-Euclidean normed spaces (and convex bodies). Roughly speaking, an n-dimensional space is λ-essentially-Euclidean (with 0 < λ < 1) if it has a [λn]dimensional subspace which has further proportionally dimensional Euclidean subspaces of any proportion. We consider a space X1 = (Rn, ‖ · ‖1) with the property that if a space X2 = (Rn, ‖ · ‖2) is “no...
متن کاملEuclidean 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...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2012
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-2011-070-9