Is a complete, reduced set necessarily of constant width?

2016/02/24 by Brandenberg, René, Merino, Bernardo González, Jahn, Thomas +1
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1602.07531

Abstract

Is it true that a convex body K being complete and reduced with respect to some gauge body C is necessarily of constant width, that is, 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.

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