Maximal Sections and Centrally Symmetric Bodies
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چکیده
Let d ≥ 2 and let K ⊂ R be a convex body containing the origin 0 in its interior. Let, for each direction ω, the (d − 1)–volume of the intersection of K and an arbitrary hyperplane with normal ω attain its maximum if the hyperplane contains 0. Then K is symmetric about 0. The proof uses a linear integro–differential operator on S, whose null–space needs to be, and will be determined.
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تاریخ انتشار 2000