Loperena, Jaime Calles
Crabb, Michael C.
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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checked on Dec 7, 2023
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