منابع مشابه
On Convex Class of Pairs of Convex Bodies
In this paper we introduce a quotient class of pairs of convex bodies in which every member have convex union. The space of pairs of convex bodies has been investigated in a number of papers [3], [8], [9], and [12]. This space has found an application in quasidifferential calculus (cf. [1], [5], [7], [10]). A quasidifferential is represented as a pair of convex bodies and it is essential to fin...
متن کاملPairs of Convex Bodies with Centrally Symmetric Intersections of Translates
For a pair of convex bodies K and K ′ in Ed , the d-dimensional intersections K ∩ (x + K ′), x ∈ Ed , are centrally symmetric if and only if K and K ′ are represented as direct sums K = R ⊕ P and K ′ = R′ ⊕ P ′ such that: (i) R is a compact convex set of some dimension m, 0 ≤ m ≤ d, and R′ = z − R for a suitable vector z ∈ Ed , (ii) P and P ′ are isothetic parallelotopes, both of dimension d − m.
متن کاملShadows of Convex Bodies
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 کاملSome extensions of the class of k-convex bodies
We study relations of some classes of k-convex, k-visible bodies in Euclidean spaces. We introduce and study circular projections in normed linear spaces and classes of bodies related with families of such maps, in particular, k-circular convex and k-circular visible ones. Investigation of these bodies more general than k-convex and k-visible ones allows us to generalize some classical results ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03959-2