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arXiv · 1612.06767

Minkowski concentricity and complete simplices

René Brandenberg·Bernardo González Merino
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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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René Brandenberg, Bernardo González Merino. 2016-12-20. Minkowski concentricity and complete simplices. https://arxiv.org/abs/1612.06767

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