Mean width inequalities for isotropic measures (Q415473)
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scientific article; zbMATH DE number 6031793
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mean width inequalities for isotropic measures |
scientific article; zbMATH DE number 6031793 |
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Mean width inequalities for isotropic measures (English)
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8 May 2012
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The authors 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 \(\ell\)-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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mean width inequality
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isotropic measure
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\(\ell \)-norm
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Ball-Barthe inequality
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