2023/03/02 by Pavle V. M. Blagojević, Blagojevic, Pavle V. M., M. C. Crabb +1 · 1 citation
Mathematics · #52A35 #55N25 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2303.01085
openalex publication_date 2023/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, extending the recent work of authors with Calles Loperena and Dimitrijević Blagojević, we give a general and complete treatment of a problem of partition of mass assignments with prescribed arrangements of hyperplanes on Euclidean vector bundles. Using a new configuration test map scheme, as well as an alternative topological framework, we are able to reprove known results, extend them to arbitrary bundles as well as to put various types of constraints on the solutions. Moreover, the developed topological methods allow us to give new proofs and extend results of Guth and Katz, Schnider, and Soberón and Takahashi. In this way we place all these results under one ``roof''.