Dual Mixed Volumes and the Slicing Problem

Details Dual Mixed Volumes and the Slicing Problem Dual Mixed Volumes and the Slicing Problem

2005-12-10

arxiv.org/abs/math/0512207v2

Mathematics

Functional Analysis

38 pages, to appear in Advances in Mathematics. Corrected Remark 4.2

Scientific paper

We develop a technique using dual mixed-volumes to study the isotropic constants of some classes of spaces. In particular, we recover, strengthen and generalize results of Ball and Junge concerning the isotropic constants of subspaces and quotients of L_p and related spaces. An extension of these results to negative values of p is also obtained, using generalized intersection-bodies. In particular, we show that the isotropic constant of a convex body which is contained in an intersection-body is bounded (up to a constant) by the ratio between the latter's mean-radius and the former's volume-radius. We also show how type or cotype 2 may be used to easily prove inequalities on any isotropic measure.

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