Cutting convex curves. (November 2016) - Holmsen, Andreas F.; Kincses, János; Roldán-Pensado, Edgardo
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 ∈ [ 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.