Projection problems for symmetric polytopes |
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Authors: | Binwu He Gangsong Leng Kanghai Li |
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Institution: | Department of Mathematics, Shanghai University, Shanghai 200444, PR China |
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Abstract: | Let K⊂Rn be a convex body (a compact, convex subset with non-empty interior), ΠK its projection body. Finding the least upper bound, as K ranges over the class of origin-symmetric convex bodies, of the affine-invariant ratio V(ΠK)/V(K)n−1, being called Schneider's projection problem, is a well-known open problem in the convex geometry. To study this problem, Lutwak, Yang and Zhang recently introduced a new affine invariant functional for convex polytopes in Rn. For origin-symmetric convex polytopes, they posed a conjecture for the new functional U(P). In this paper, we give an affirmative answer to the conjecture in Rn, thereby, obtain a modified version of Schneider's projection problem. |
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Keywords: | 52A40 |
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