The convex intersection body of a convex body

Mathieu Meyer; Shlomo Reisner

doi:10.1017/S0017089511000103

The convex intersection body of a convex body

Mathieu Meyer, Shlomo Reisner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let L be a convex body in Rⁿ and z an interior point of L. We associate with L and z a new, convex and centrally symmetric, body CI(L, z). This generalizes the classical intersection body I(L, z) (whose radial function at u∈S^n-1 is the volume of the hyperplane section of L through z, orthogonal to u). CI(L, z) coincides with I(L, z) if and only if L is centrally symmetric about z. We study the properties of CI(L, z).

Original language	English
Pages (from-to)	523-534
Number of pages	12
Journal	Glasgow Mathematical Journal
Volume	53
Issue number	3
DOIs	https://doi.org/10.1017/S0017089511000103
State	Published - 1 Sep 2011

Bibliographical note

Publisher Copyright:
Copyright © Glasgow Mathematical Journal Trust 2011.

ASJC Scopus subject areas

General Mathematics

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10.1017/S0017089511000103

Cite this

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abstract = "Let L be a convex body in Rn and z an interior point of L. We associate with L and z a new, convex and centrally symmetric, body CI(L, z). This generalizes the classical intersection body I(L, z) (whose radial function at u∈Sn-1 is the volume of the hyperplane section of L through z, orthogonal to u). CI(L, z) coincides with I(L, z) if and only if L is centrally symmetric about z. We study the properties of CI(L, z).",

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AB - Let L be a convex body in Rn and z an interior point of L. We associate with L and z a new, convex and centrally symmetric, body CI(L, z). This generalizes the classical intersection body I(L, z) (whose radial function at u∈Sn-1 is the volume of the hyperplane section of L through z, orthogonal to u). CI(L, z) coincides with I(L, z) if and only if L is centrally symmetric about z. We study the properties of CI(L, z).

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The convex intersection body of a convex body

Abstract

Bibliographical note

ASJC Scopus subject areas

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