Jung-type Inequalities and Blaschke-Santal\'o Diagrams for Different Diameter Variants
Metric Geometry
2025-12-03 v2
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 and its origin reflection .
Keywords
Cite
@article{arxiv.2309.12092,
title = {Jung-type Inequalities and Blaschke-Santal\'o Diagrams for Different Diameter Variants},
author = {René Brandenberg and Mia Runge},
journal= {arXiv preprint arXiv:2309.12092},
year = {2025}
}