Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions

Oleg R. Musin

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arXiv · 2603.18550

Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions

Oleg R. Musin

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Abstract

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.

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BibTeX RIS

Oleg R. Musin. 2026-03-19. Borsuk-Ulam type theorem for Stiefel manifolds and orthogonal mass partitions. https://arxiv.org/abs/2603.18550

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