THE CONVEX INTERSECTION BODY OF A CONVEX BODY

Mathieu Meyer (1) , Shlomo Reisner

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

Let L be a convex body in R(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 body I(L, z) (whose radial function at u is an element of 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).

Domaines: Physique mathématique [math-ph]

Mathieu Meyer, Shlomo Reisner. THE CONVEX INTERSECTION BODY OF A CONVEX BODY. Glasgow Mathematical Journal, 2011, 53 (?), pp.523--534. ⟨10.1017/S0017089511000103⟩. ⟨hal-00692820⟩