A hyperplane Ham Sandwich theorem
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910381274824704 |
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| author | Crabb, M. C. |
| author_facet | Crabb, M. C. |
| contents | We give a direct proof of a result due to Karasev (2008), Karasev-Matschke (2014) and Schnider-Soberón (2023). Given $m+1$ Borel probability measures on the space of affine hyperplanes in a real vector space $V$ of dimension $m+1$, there exist a line $L$ through the origin in $V$ and a point $v\in L$ such that at least half of the hyperplanes, as counted by any of the measures, meet or are parallel to each of the two closed rays in $L$ meeting at $v$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A hyperplane Ham Sandwich theorem Crabb, M. C. Geometric Topology 52A20, 52A35, 52C35, 55M25, 55N25 We give a direct proof of a result due to Karasev (2008), Karasev-Matschke (2014) and Schnider-Soberón (2023). Given $m+1$ Borel probability measures on the space of affine hyperplanes in a real vector space $V$ of dimension $m+1$, there exist a line $L$ through the origin in $V$ and a point $v\in L$ such that at least half of the hyperplanes, as counted by any of the measures, meet or are parallel to each of the two closed rays in $L$ meeting at $v$. |
| title | A hyperplane Ham Sandwich theorem |
| topic | Geometric Topology 52A20, 52A35, 52C35, 55M25, 55N25 |
| url | https://arxiv.org/abs/2403.08794 |