A generalization of Grünbaum's inequality
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910643523682304 |
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| author | Letwin, Brayden Yaskin, Vladyslav |
| author_facet | Letwin, Brayden Yaskin, Vladyslav |
| contents | Grünbaum's inequality gives sharp bounds between the volume of a convex body and its part cut off by a hyperplane through the centroid of the body. We provide a generalization of this inequality for hyperplanes that do not necessarily contain the centroid. As an application, we obtain a sharp inequality that compares sections of a convex body to the maximal section parallel to it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04741 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generalization of Grünbaum's inequality Letwin, Brayden Yaskin, Vladyslav Metric Geometry 52A20 (Primary) Grünbaum's inequality gives sharp bounds between the volume of a convex body and its part cut off by a hyperplane through the centroid of the body. We provide a generalization of this inequality for hyperplanes that do not necessarily contain the centroid. As an application, we obtain a sharp inequality that compares sections of a convex body to the maximal section parallel to it. |
| title | A generalization of Grünbaum's inequality |
| topic | Metric Geometry 52A20 (Primary) |
| url | https://arxiv.org/abs/2410.04741 |