Extremal spherical polytopes and Borsuk's conjecture
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866929584078848000 |
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| author | Katz, Mikhail Mémoli, Facundo Wang, Qingsong |
| author_facet | Katz, Mikhail Mémoli, Facundo Wang, Qingsong |
| contents | We generate anti-self-polar polytopes via a numerical implementation of the gradient flow induced by the diameter functional on the space of all finite subsets of the sphere, and prove related results on the critical points of the diameter functional as well as results about the combinatorics of such polytopes. We also discuss potential connections to Borsuk's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_13076 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extremal spherical polytopes and Borsuk's conjecture Katz, Mikhail Mémoli, Facundo Wang, Qingsong Combinatorics Metric Geometry We generate anti-self-polar polytopes via a numerical implementation of the gradient flow induced by the diameter functional on the space of all finite subsets of the sphere, and prove related results on the critical points of the diameter functional as well as results about the combinatorics of such polytopes. We also discuss potential connections to Borsuk's conjecture. |
| title | Extremal spherical polytopes and Borsuk's conjecture |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2301.13076 |