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arXiv · 1105.2629

Isomorphic properties of Intersection bodies

A. Koldobsky·G. Paouris·M. Zymonopoulou
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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.

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A. Koldobsky, G. Paouris, M. Zymonopoulou. 2011-05-13. Isomorphic properties of Intersection bodies. https://arxiv.org/abs/1105.2629

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