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arXiv · 2309.12092

Jung-type Inequalities and Blaschke-Santal\'o Diagrams for Different Diameter Variants

René Brandenberg·Mia Runge
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Abstract

We study geometric inequalities for the circumradius and diameter with respect to general gauges, partly also involving the inradius and the Minkowski asymmetry. There are a number of options for defining the diameter of a convex body that fall apart when we consider non-symmetric gauges. These definitions correspond to different symmetrizations of the gauge, i.e. means of the gauge $C$ and its origin reflection $-C$.

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René Brandenberg, Mia Runge. 2023-09-21. Jung-type Inequalities and Blaschke-Santal\'o Diagrams for Different Diameter Variants. https://doi.org/10.1016/j.nuclphysb.2023.116421

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