Many partitions of mass assignments

In this paper, extending the recent work of the authors with Calles Loperena and Dimitrijević Blagojević, we give a general and complete treatment of problems 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”.