Document Type

Article

Publication Date

3-1994

Keywords

Convex body, Section, Busemann-Petty problem, Intersection body

Abstract

It is proved that the answer to the Busemann-Petty problem concerning central sections of centrally symmetric convex bodies in d-dimensional Euclidean space Ed is negative for a given d if and only if certain centrally symmetric convex bodies exist in Ed which are not intersection bodies. It is also shown that a cylinder in Ed is an intersection body if and only if d ≤ 4, and that suitably smooth axis-convex bodies of revolution are intersection bodies when d ≤ 4. These results show that the Busemann-Petty problem has a negative answer for d ≥ 5 and a positive answer for d = 3 and d = 4 when the body with smaller sections is a body of revolution.

Publication Title

Transactions of the American Mathematical Society

Volume

342

Issue

1

First Page

435

Last Page

445

Required Publisher's Statement

First published in Transactions of the American Mathematical Society in Volume 342, Number 1, March 1994, published by the American Mathematical Society

Subjects - Topical (LCSH)

Convex bodies; Intersection theory (Mathematics)

Genre/Form

articles

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

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Included in

Mathematics Commons

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