On Maximal k-Sections and Related Common Transversals of Convex Bodies

Abstract

AbstractGeneralizing results from [MM1] referring to the intersection body IK and the cross-section body CK of a convex body K ⊂ , d ≥ 2, we prove theorems about maximal k-sections of convex bodies, k ∈ {1, … ,d − 1}, and, simultaneously, statements about common maximal (d − 1)- and 1-transversals of families of convex bodies.