Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915649259831296 |
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| author | Brandenberg, René Runge, Mia |
| author_facet | Brandenberg, René Runge, Mia |
| contents | 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 $-C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12092 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants Brandenberg, René Runge, Mia Metric Geometry 52A40 (Primary) 52A10 (Secondary) 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 $-C$. |
| title | Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants |
| topic | Metric Geometry 52A40 (Primary) 52A10 (Secondary) |
| url | https://arxiv.org/abs/2309.12092 |