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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/2312.10574 |
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| _version_ | 1866916369099915264 |
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| author | Reuter, Chase |
| author_facet | Reuter, Chase |
| contents | We prove that, in a neighborhood of the Euclidean ball, there are no other fixed points of the $p$-centroid body operator, using spherical harmonic techniques. We also show that the Euclidean ball is locally the only body whose centroid body is a dilate of its polar intersection body. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10574 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local fixed point results for centroid body operators Reuter, Chase Metric Geometry 52A20, 33C55, 44A12 We prove that, in a neighborhood of the Euclidean ball, there are no other fixed points of the $p$-centroid body operator, using spherical harmonic techniques. We also show that the Euclidean ball is locally the only body whose centroid body is a dilate of its polar intersection body. |
| title | Local fixed point results for centroid body operators |
| topic | Metric Geometry 52A20, 33C55, 44A12 |
| url | https://arxiv.org/abs/2312.10574 |