Bounding the diameter-width ratio using containment inequalities of means of convex bodies
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908693803565056 |
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| author | von Dichter, Katherina Runge, Mia |
| author_facet | von Dichter, Katherina Runge, Mia |
| contents | We completely describe the region of possible values of the diameter-width ratio for planar pseudo-complete sets in dependence of the Minkowski asymmetry. In order to do this, we focus on the containment inequalities of $K \cap (-K)$ and $\frac{K-K}{2}$ for a Minkowski centered convex compact set $K$, i.e. we define $τ(K)$ to be the smallest possible factor to cover $K \cap (-K)$ by a rescalation of $\frac{K-K}{2}$ and give the region of the possible values of $τ(K)$ in the planar case in dependence of the Minkowski asymmetry of $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounding the diameter-width ratio using containment inequalities of means of convex bodies von Dichter, Katherina Runge, Mia Metric Geometry 52A40, 52A10 We completely describe the region of possible values of the diameter-width ratio for planar pseudo-complete sets in dependence of the Minkowski asymmetry. In order to do this, we focus on the containment inequalities of $K \cap (-K)$ and $\frac{K-K}{2}$ for a Minkowski centered convex compact set $K$, i.e. we define $τ(K)$ to be the smallest possible factor to cover $K \cap (-K)$ by a rescalation of $\frac{K-K}{2}$ and give the region of the possible values of $τ(K)$ in the planar case in dependence of the Minkowski asymmetry of $K$. |
| title | Bounding the diameter-width ratio using containment inequalities of means of convex bodies |
| topic | Metric Geometry 52A40, 52A10 |
| url | https://arxiv.org/abs/2512.04633 |