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arXiv · 2509.05028

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

René Brandenberg·Bernardo González Merino·Mia Runge
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Abstract

We present a complete system of inequalities for the inradius, circumradius, and diameter in the $3$-dimensional Euclidean space. To do so, we prove quasiconcavity of the inradius evaluated over $n$-simplices with a common facet independently of the norm/gauge under consideration.

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René Brandenberg, Bernardo González Merino, Mia Runge. 2025-09-05. A complete system of inequalities for the diameter, in-, and circumradius in the 3-dimensional Euclidean space. https://arxiv.org/abs/2509.05028

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