Mean width inequalities for isotropic measures
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.
scientific article; zbMATH DE number 6031793
scientific article