On the Asymmetry Constant of a Body with Few Vertices |
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| Authors: | E D Gluskin A E Litvak |
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| Institution: | (1) Department of Mathematics, Tel Aviv University, Tel Aviv, Israel;(2) Department of Mathematics, Technion, Haifa, Israel;(3) Present address: Department of Math. and Stat. Sc., Univ. of Alberta, Edmonton, AB, Canada, T6G 2G1 |
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| Abstract: | In this note, we show that a nondegenerated polytope in IR
n
with n + k, 1  k < n, vertices is far from any symmetric body. We provide the asymptotically sharp estimates for the asymmetry constant of such polytopes. |
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| Keywords: | convex bodies Banach– Mazur distance asymmetry constant polytopes affine transformation |
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