Covering shadows with a smaller volume
نویسندگان
چکیده
منابع مشابه
Covering shadows with a smaller volume
For n ≥ 2 a construction is given for convex bodies K and L in R n such that the orthogonal projection Ku can be translated inside Lu for every direction u, while the volumes of K and L satisfy Vn(K) > Vn(L). A more general construction is then given for n-dimensional convex bodies K and L such that the orthogonal projection Kξ can be translated inside Lξ for every k-dimensional subspace ξ of R...
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We give an explicit upper bound of the minimal number νT,n of balls of radius 1/2 which form a covering of a ball of radius T > 1/2 in R , n > 2. The asymptotic estimates of νT,n we deduce when n is large are improved further by recent results of Böröczky Jr. and Wintsche on the asymptotic estimates of the minimal number of equal balls of R n covering the sphere S. The optimality of the asympto...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2010
ISSN: 0001-8708
DOI: 10.1016/j.aim.2009.12.008