Isomorphic properties of Intersection bodies
Functional Analysis
2011-05-16 v1
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.
Cite
@article{arxiv.1105.2629,
title = {Isomorphic properties of Intersection bodies},
author = {A. Koldobsky and G. Paouris and M. Zymonopoulou},
journal= {arXiv preprint arXiv:1105.2629},
year = {2011}
}