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Holmsen, Andreas F.,Kincses, Já,nos,Roldá,n-Pensado, Edgardo Elsevier 2016 European journal of combinatorics : Journal europ& Vol.58 No.-
<P><B>Abstract</B></P> <P>We show that for any two convex curves <SUB> C 1 </SUB> and <SUB> C 2 </SUB> in <SUP> R d </SUP> parametrized by [ 0 , 1 ] with opposite orientations, there exists a hyperplane H with the following property: For any t ∈ [ 0 , 1 ] the points <SUB> C 1 </SUB> ( t ) and <SUB> C 2 </SUB> ( 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.</P>