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).
Bibliographical notePublisher Copyright:
Copyright © Glasgow Mathematical Journal Trust 2011.
ASJC Scopus subject areas
- Mathematics (all)