Reductibility of Convex Bodies
نویسنده
چکیده
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 about centre 6 in B. The sets C(r) are defined as follows:
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