[Banach] Abstract of a paper by Boaz Klartag and Emanuel Milman

[Dale Alspach]

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 at weizmann.ac.il

The paper may be downloaded from the archive by web browser from
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 http://front.math.ucdavis.edu/math.FA/0604594

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 http://arXiv.org/abs/math.FA/0604594

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