Brandenberg, R.; B. González Merino, T. Jahn and H. Martini
Is a complete, reduced set necessarily of constant width?
Is it true that a convex body K being complete and reduced with respect to some gauge body C is necessarily of constant width, i. e., satisfies K − K = ρ(C − C) for some ρ > 0? We prove this implication for several cases including the following: if K is a simplex and or if K possesses a smooth extreme point, then the implication holds. Moreover, we derive several new results on perfect norms.
Advances in Geometry
Lehrstuhl für Angewandte Geometrie und Diskrete Mathematik