论文标题
加强了平均宽度和$ \ ell $ norm的不平等现象
Strengthened inequalities for the mean width and the $\ell$-norm
论文作者
论文摘要
Barthe证明，常规的单纯形可以最大程度地提高凸形体的平均宽度，其John Ellipsoid（人体中包含的最大体积椭圆形）是欧几里得单位球；或同等地，常规的单纯形使凸体的$ \ ell $ norm最大化，凸体的löwner椭圆形（最小含有身体的椭圆形）是欧几里得单位球。 Schmuckenschläger验证了反向语句；也就是说，常规的单纯形可以最大程度地减少凸体的平均宽度，而凸体的löwner椭圆形是欧几里得单位球。在这里，我们证明了这些结果的更强稳定性版本。我们还考虑了平均宽度和$ \ ell $ norm的相关稳定性结果。
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 Löwner ellipsoid (minimal volume ellipsoid containing the body) is the Euclidean unit ball. Schmuckenschläger verified the reverse statement; namely, the regular simplex minimizes the mean width of convex bodies whose Löwner ellipsoid is the Euclidean unit ball. Here we prove stronger stability versions of these results. We also consider related stability results for the mean width and the $\ell$-norm of the convex hull of the support of centered isotropic measures on the unit sphere.
