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Document type:
Zeitschriftenaufsatz 
Author(s):
Brandenberg, R.; B. González Merino, T. Jahn and H. Martini 
Title:
Is a complete, reduced set necessarily of constant width? 
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, 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. 
Journal title:
Advances in Geometry 
Year:
2017 
Reviewed:
ja 
Language:
en 
Publisher:
De Gruyter 
TUM Institution:
Lehrstuhl für Angewandte Geometrie und Diskrete Mathematik