On volume distribution in 2-convex bodies

Details On volume distribution in 2-convex bodies On volume distribution in 2-convex bodies

2006-04-27

arxiv.org/abs/math/0604594v1

Mathematics

Functional Analysis

27 pages

Scientific paper

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

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