A characterization of centrally symmetric convex bodies in terms of visual cones
نویسندگان
چکیده
Abstract We prove the following result: Let K be a strictly convex body in Euclidean space ℝ n , ≥ 3, and let L hypersurface which is image of an embedding sphere
منابع مشابه
Pairs 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.
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چکیده ندارد.
15 صفحه اولUPPER BOUNDS FOR THE COVERING NUMBER OF CENTRALLY SYMMETRIC CONVEX BODIES IN Rn
The covering number c(K) of a convex body K is the least number of smaller homothetic copies of K needed to cover K . We provide new upper bounds for c(K) when K is centrally symmetric by introducing and studying the generalized α -blocking number βα 2 (K) of K . It is shown that when a centrally symmetric convex body K is sufficiently close to a centrally symmetric convex body K′ , then c(K) i...
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ژورنال
عنوان ژورنال: Advances in Geometry
سال: 2022
ISSN: ['1615-715X', '1615-7168']
DOI: https://doi.org/10.1515/advgeom-2022-0006