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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.07074 |
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| _version_ | 1866929355678023680 |
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| author | Zawalski, Bartłomiej |
| author_facet | Zawalski, Bartłomiej |
| contents | We will prove that an origin-symmetric star-convex body $K$ with sufficiently smooth boundary and such that every hyperplane section of $K$ passing through the origin is a body of affine revolution, is itself a body of affine revolution. This will give a positive answer to the recent question asked by G. Bor, L. Hernández-Lamoneda, V. Jiménez de Santiago, and L. Montejano-Peimbert, though with slightly different prerequisites. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07074 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On star-convex bodies with rotationally invariant sections Zawalski, Bartłomiej Metric Geometry Primary 53A07, Secondary 12D10, 53A15 We will prove that an origin-symmetric star-convex body $K$ with sufficiently smooth boundary and such that every hyperplane section of $K$ passing through the origin is a body of affine revolution, is itself a body of affine revolution. This will give a positive answer to the recent question asked by G. Bor, L. Hernández-Lamoneda, V. Jiménez de Santiago, and L. Montejano-Peimbert, though with slightly different prerequisites. |
| title | On star-convex bodies with rotationally invariant sections |
| topic | Metric Geometry Primary 53A07, Secondary 12D10, 53A15 |
| url | https://arxiv.org/abs/2304.07074 |