Answers to questions of Grünbaum and Loewner
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916472265113600 |
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| author | Myroshnychenko, S. Tatarko, K. Yaskin, V. |
| author_facet | Myroshnychenko, S. Tatarko, K. Yaskin, V. |
| contents | We construct a convex body $K$ in $\mathbb{R}^n$, $n \geq 5$, with the property that there is exactly one hyperplane $H$ passing through $c(K)$, the centroid of $K$, such that the centroid of $K\cap H$ coincides with $c(K)$. This provides answers to questions of Grünbaum and Loewner for $n\geq 5$. The proof is based on the existence of non-intersection bodies in these dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Answers to questions of Grünbaum and Loewner Myroshnychenko, S. Tatarko, K. Yaskin, V. Metric Geometry Functional Analysis 52A20, 52A40 We construct a convex body $K$ in $\mathbb{R}^n$, $n \geq 5$, with the property that there is exactly one hyperplane $H$ passing through $c(K)$, the centroid of $K$, such that the centroid of $K\cap H$ coincides with $c(K)$. This provides answers to questions of Grünbaum and Loewner for $n\geq 5$. The proof is based on the existence of non-intersection bodies in these dimensions. |
| title | Answers to questions of Grünbaum and Loewner |
| topic | Metric Geometry Functional Analysis 52A20, 52A40 |
| url | https://arxiv.org/abs/2404.15188 |