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arXiv · 2507.06919

Partitions of mass assignments with spheres and wedges

Deron Lessure·Pablo Soberón
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Abstract

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.

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Deron Lessure, Pablo Soberón. 2025-07-09. Partitions of mass assignments with spheres and wedges. https://arxiv.org/abs/2507.06919

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