Strengthened inequalities for the mean width and the $ell$-norm


Abstract in English

Barthe proved that the regular simplex maximizes the mean width of convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the body) is the Euclidean unit ball; or equivalently, the regular simplex maximizes the $ell$-norm of convex bodies whose Lowner ellipsoid (minimal volume ellipsoid containing the body) is the Euclidean unit ball. Schmuckenschlager verified the reverse statement; namely, the regular simplex minimizes the mean width of convex bodies whose Lowner ellipsoid is the Euclidean unit ball. Here we prove stronger stabili

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