Extremal Distances between Sections of Convex Bodies
نویسنده
چکیده
Let K, D be convex centrally symmetric bodies in R. Let k < n and let dk(K, D) be the smallest Banach–Mazur distance between k-dimensional sections of K and D. Define ∆(k, n) = sup dk(K, D), where the supremum is taken over all n−dimensional convex symmetric bodies K, D. We prove that for any k < n ∆(k, n) ∼log n {√ k if k ≤ n k2 n if k > n , where A ∼log n B means that 1/(C log n) ·A ≤ B ≤ (C log n) ·A for some absolute constants C, a > 0.
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