Topology of the Grünbaum-Hadwiger-Ramos problem for mass assignments - Blagojević, Pavle V. M.; Loperena, Jaime Calles; Crabb, Michael C.; Dimitrijević Blagojević, Aleksandra S. (Topological Methods in Nonlinear Analysis, 2023)
In this paper, motivated by recent work of Schnider and Axelrod-Freed and Soberón, we study an extension of the classical Grünbaum-Hadwiger-Ramos mass partition problem to mass assignments. Using the Fadell-Husseini index theory we prove that for a given family of j mass assignments μ_1,…,μ_j on the Grassmann manifold G_(R^d) and a given integer k≥ 1 there exist a linear subspace LG_(R^d) and k affine hyperplanes in L that equipart the masses μ_1^L,…,μ_j^L assigned to the subspace L, provided that d≥ j + (2^k-1-1)2^_2j floor.