Type: Article

Cutting convex curves

Holmsen, Andreas F.; Kincses, János; Roldán-Pensado, Edgardo;

Abstract:

We show that for any two convex curves and in parametrized by with opposite orientations, there exists a hyperplane with the following property: For any the points and are never in the same open half space bounded by . This will be deduced from a more general result on equipartitions of ordered point sets by hyperplanes.