Minkowski concentricity and complete simplices
Metric Geometry
2016-12-21 v1
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.
Keywords
Cite
@article{arxiv.1612.06767,
title = {Minkowski concentricity and complete simplices},
author = {René Brandenberg and Bernardo González Merino},
journal= {arXiv preprint arXiv:1612.06767},
year = {2016}
}