Authors: Blagojević, Pavle 
Loperena, Jaime Calles
Crabb, Michael C.
Dimitrijević-Blagojević, Aleksandra 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: TOPOLOGY OF THE GRÜNBAUM–HADWIGER–RAMOS PROBLEM FOR MASS ASSIGNMENTS
Journal: Topological Methods in Nonlinear Analysis
Volume: 61
Issue: 1
First page: 107
Last page: 133
Issue Date: 2023
Rank: ~M22
ISSN: 1230-3429
DOI: 10.12775/TMNA.2022.041
Abstract: 
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 µ1, …, µj on the Grassmann manifold GℓRd) and (a given integer k ≥ 1 there exist a linear subspace L ∈ GℓRd) and k affine hyperplanes in L that equipart the masses µL1, …, µLj assigned to the subspace L, provided that d ≥ j + (2k−1 − 1)2⌊log 2j⌋.
Keywords: existence of equivariant maps | Fadell–Husseini ideal valued index | Mass partitions
Publisher: Juliusz Schauder Center for Nonlinear Analysis

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