This is an announcement for the paper "Relative entropy of cone measures and $L_p$ centroid bodies" by Grigoris Paouris and Elisabeth M. Werner.
Abstract: Let $K$ be a convex body in $\mathbb R^n$. We introduce a new affine invariant, which we call $\Omega_K$, that can be found in three different ways: as a limit of normalized $L_p$-affine surface areas, as the relative entropy of the cone measure of $K$ and the cone measure of $K^\circ$, as the limit of the volume difference of $K$ and $L_p$-centroid bodies. We investigate properties of $\Omega_K$ and of related new invariant quantities. In particular, we show new affine isoperimetric inequalities and we show a "information inequality" for convex bodies.
Archive classification: math.FA
Mathematics Subject Classification: 52A20, 53A15
The source file(s), PaourWern.tex: 116056 bytes, is(are) stored in gzipped form as 0909.4361.gz with size 27kb. The corresponding postcript file has gzipped size 188kb.
Submitted from: elisabeth.werner@case.edu
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