Minkowski concentricity and complete simplices

2016/12/20 by Brandenberg, René, Merino, Bernardo González · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1612.06767

Abstract

This paper considers the radii functionals (circumradius, inradius, and diameter) as well as the Minkowski asymmetry for general (possibly non-symmetric) gauge bodies. A generalization of the concentricity inequality (which states that the sum of the inradius and circumradius is not greater than the diameter in general Minkowski spaces) for non-symmetric gauge bodies is derived and a strong connection between this new inequality, extremal sets of the generalized Bohnenblust inequality, and completeness of simplices is revealed.

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• A complete system of inequalities for the diameter, in-, and circumradius in the 3-dimensional Euclidean space

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