This is an announcement for the paper "Isomorphic properties of intersection bodies" by A. Koldobsky, G. Paouris and M. Zymonopoulou.
Abstract: We study isomorphic properties of two generalizations of intersection bodies, the class of k-intersection bodies and the class of generalized k-intersection bodies. We also show that the Banach-Mazur distance of the k-intersection body of a convex body, when it exists and it is convex, with the Euclidean ball, is bounded by a constant depending only on k, generalizing a well-known result of Hensley and Borell. We conclude by giving some volumetric estimates for k-intersection bodies.
Archive classification: math.FA
Submitted from: marisa.zym@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.2629
or