This is an announcement for the paper "On volume distribution in 2-convex bodies" by Boaz Klartag and Emanuel Milman.
Abstract: 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 L_p and S_p^m, the Schatten Class space.
Archive classification: Functional Analysis; Metric Geometry
Remarks: 27 pages
The source file(s), 2-Convex-Bodies.bbl: 7979 bytes, 2-Convex-Bodies.tex: 70706 bytes, is(are) stored in gzipped form as 0604594.tar.gz with size 24kb. The corresponding postcript file has gzipped size 104kb.
Submitted from: emanuel.milman@weizmann.ac.il
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