Mean width inequalities for isotropic measures |
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Authors: | Ai-Jun Li Gangsong Leng |
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Institution: | 1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, China 2. Department of Mathematics, Shanghai University, Shanghai, 200444, China
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Abstract: | In this paper, we establish Barthe’s mean width inequalities for continuous isotropic measures by a direct approach rather than using the Brascamp–Lieb inequality. The following results are obtained: among the convex hulls of the support of isotropic measures on S n–1, the regular simplex inscribed in the Euclidean unit ball has maximal ?-norm; in the dual situation, there is a reverse result for their polar bodies. Moreover, the case of even isotropic measures is also investigated. |
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