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arXiv · 1502.07602

Complete sets need not be reduced in Minkowski spaces

Horst Martini·Senlin Wu
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Abstract

It is well known that in $n$-dimensional Euclidean space ($n\geq 2$) the classes of (diametrically) complete sets and of bodies of constant width coincide. Due to this, they both form a proper subfamily of the class of reduced bodies. For $n$-dimensional Minkowski spaces, this coincidence is no longer true if $n\geq 3$. Thus, the question occurs whether for $n\geq 3$ any complete set is reduced. Answering this in the negative for $n\geq 3$, we construct $(2^{k}-1)$-dimensional ($k\geq 2$) complete sets which are not reduced.

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Horst Martini, Senlin Wu. 2015-02-25. Complete sets need not be reduced in Minkowski spaces. https://doi.org/10.1007/s13366-015-0249-3

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