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).
Original language | English |
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Pages (from-to) | 523-534 |
Number of pages | 12 |
Journal | Glasgow Mathematical Journal |
Volume | 53 |
Issue number | 3 |
DOIs | |
State | Published - 1 Sep 2011 |
Bibliographical note
Publisher Copyright:Copyright © Glasgow Mathematical Journal Trust 2011.
ASJC Scopus subject areas
- General Mathematics