Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910251830214656 |
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| author | Musin, Oleg R. |
| author_facet | Musin, Oleg R. |
| contents | A generalization of the Borsuk-Ulam theorem to Stiefel manifolds is considered. This theorem is applied to derive bounds on $d$ that guarantee-for a given set of $m$ measures in $\mathbb{R}^d$-the existence of $k$ mutually orthogonal hyperplanes, any $n$ of which partition each of the measures into $2^n$ equal parts. If $n=k$, the result corresponds to the bound obtained in [14], but with the stronger conclusion that the hyperplanes are mutually orthogonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18550 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions Musin, Oleg R. Algebraic Topology Combinatorics Metric Geometry A generalization of the Borsuk-Ulam theorem to Stiefel manifolds is considered. This theorem is applied to derive bounds on $d$ that guarantee-for a given set of $m$ measures in $\mathbb{R}^d$-the existence of $k$ mutually orthogonal hyperplanes, any $n$ of which partition each of the measures into $2^n$ equal parts. If $n=k$, the result corresponds to the bound obtained in [14], but with the stronger conclusion that the hyperplanes are mutually orthogonal. |
| title | Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions |
| topic | Algebraic Topology Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2603.18550 |