Bredon cohomology methods in mass partition problems on spheres

Abstract

We apply $\mathrm{RO}(G)$-graded Bredon cohomology to mass assignment problems, extending classical mass partition methods. Within this framework, we reprove a recent result of Lessure and Soberón: for $n+1$ mass assignments on $k$-dimensional affine subspaces of ${\mathbb{R}}^n$, there exists a $k$-subspace containing a sphere that simultaneously bisects all measures. This approach highlights a flexible topological framework with potential for broader applications.

13 pages, accepted in HHA