Cutting convex curves

Abstract

We show that for any two convex curves C-1 and C-2 in R-d parametrized by [0, 1] with opposite orientations, there exists a hyperplane H with the following property: For any t is an element of [0, 1] the points C-1 (t) and C-2(t) are never in the same open half space bounded by H. This will be deduced from a more general result on equipartitions of ordered point sets by hyperplanes. (C) 2016 Elsevier Ltd. All rights reserved.