This is an announcement for the paper "Dual mixed volumes and the slicing problem" by Emanuel Milman.
Abstract: 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.
Archive classification: Functional Analysis; Metric Geometry
Remarks: 38 pages, to appear in Advance in Mathematics
The source file(s), dual-mixed-volumes-and-slicing-problem-for-arxiv.bbl: 7985 bytes, dual-mixed-volumes-and-slicing-problem-for-arxiv.tex: 94404 bytes, is(are) stored in gzipped form as 0512207.tar.gz with size 29kb. The corresponding postcript file has gzipped size 130kb.
Submitted from: emanuel.milman@weizmann.ac.il
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