On bodies in [formula omitted] with congruent sections by cones or non-central planes

Abstract

Let K and L be two convex bodies in Rn, n≥3 such that their sections by cones {x∈Rn:x⋅ξ=t|x|} or non-central planes with a fixed distance from the origin are directly congruent. We prove that if their boundaries are of class C2, then K and L coincide.