THE CONVEX INTERSECTION BODY OF A CONVEX BODY

摘要

Abstract. Let L be a convex body in u0002nnand z an interior point of L.We associatenwith L and z a new, convex and centrally symmetric, body CI(L, z). This generalizesnthe classical intersection body I(L, z) (whose radial function at u ∈ Sn−1nis the volumenof the hyperplane section of L through z, orthogonal to u). CI(L, z) coincides withnI(L, z) if and only if L is centrally symmetric about z. We study the properties ofnCI(L, z).