Partitions of mass assignments with spheres and wedges
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913943372431360 |
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| author | Lessure, Deron Soberón, Pablo |
| author_facet | Lessure, Deron Soberón, Pablo |
| contents | In this paper, we generalize classic mass partition results dealing with partitions using spheres, parallel hyperplanes, or axis-parallel wedges to the setting of mass assignments. In a mass assignment problem, we assign mass distributions continuously to all $k$-dimensional subspaces of $\mathbb{R}^d$, and seek to guarantee the existence of a particular subspace in which more masses can be bisected than those by analyzing the problem in $\mathbb{R}^k$. We prove new mass assignment results for spheres, parallel hyperplanes, and axis-parallel wedges. The proof techniques rely on new Borsuk--Ulam type theorems on spheres and Stiefel manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partitions of mass assignments with spheres and wedges Lessure, Deron Soberón, Pablo Combinatorics Algebraic Topology 52C35, 52A37, 28A75 In this paper, we generalize classic mass partition results dealing with partitions using spheres, parallel hyperplanes, or axis-parallel wedges to the setting of mass assignments. In a mass assignment problem, we assign mass distributions continuously to all $k$-dimensional subspaces of $\mathbb{R}^d$, and seek to guarantee the existence of a particular subspace in which more masses can be bisected than those by analyzing the problem in $\mathbb{R}^k$. We prove new mass assignment results for spheres, parallel hyperplanes, and axis-parallel wedges. The proof techniques rely on new Borsuk--Ulam type theorems on spheres and Stiefel manifolds. |
| title | Partitions of mass assignments with spheres and wedges |
| topic | Combinatorics Algebraic Topology 52C35, 52A37, 28A75 |
| url | https://arxiv.org/abs/2507.06919 |