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THE CONVEX INTERSECTION BODY OF A CONVEX BODY

Published online by Cambridge University Press:  10 March 2011

MATHIEU MEYER  and
SHLOMO REISNER
MATHIEU MEYER
Affiliation:
Université Paris-Est - Marne-la-Vallée, Laboratoire d'Analyse et de Mathématiques Appliquées (UMR 8050), Cité Descartes, 5 Bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée cedex 2, France e-mail: [email protected]
SHLOMO REISNER
Affiliation:
Department of Mathematics, University of Haifa, Haifa 31905, Israel e-mail: [email protected]
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Abstract

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Let L be a convex body in n 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 bodyI(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).

Keywords

52A20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 3 , September 2011 , pp. 523 - 534
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

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