On Volume Distribution in 2-convex Bodies
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چکیده
We consider convex sets whose modulus of convexity is uniformly quadratic. First, we observe several interesting relations between different positions of such “2-convex” bodies; in particular, the isotropic position is a finite volume-ratio position for these bodies. Second, we prove that high dimensional 2-convex bodies posses one-dimensional marginals that are approximately Gaussian. Third, we improve for 1 < p ≤ 2 some bounds on the isotropic constant of quotients of subspaces of Lp and S m p , the Schatten Class space.
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