An isomorphic version of the slicing problem |
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Authors: | B Klartag |
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Institution: | School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel |
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Abstract: | Here we show that any centrally-symmetric convex body has a perturbation which is convex and centrally-symmetric, such that the isotropic constant of T is universally bounded. T is close to K in the sense that the Banach-Mazur distance between T and K is . If K is a body of a non-trivial type then the distance is universally bounded. The distance is also universally bounded if the perturbation T is allowed to be non-convex. Our technique involves the use of mixed volumes and Alexandrov-Fenchel inequalities. Some additional applications of this technique are presented here. |
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Keywords: | Convex bodies Hyperplane sections The slicing problem Alexandrov-Fenchel inequalities |
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