A Center Transversal Theorem for mass assignments
Classical Analysis and ODEs
2025-03-31 v3 Functional Analysis
Metric Geometry
Abstract
In this paper, based on the ideas of Blagojevi\'c, Karasev & Magazinov, we consider an extension of the center transversal theorem to mass assignments with an improved Rado depth. In particular we substitute the marginal of a measure by a more general concept called a mass assignment over a flag manifold. Our results also allow us to solve the main problem proposed by Blagojevi\'c, Karasev & Magazinov in a linear subspace of lower dimension, as long as it is contained in a high-dimensional enough ambient space.
Cite
@article{arxiv.2401.15095,
title = {A Center Transversal Theorem for mass assignments},
author = {Omar Antolín Camarena and Jaime Calles Loperena},
journal= {arXiv preprint arXiv:2401.15095},
year = {2025}
}
Comments
We present a slight generalization of theorem 2.4, as well as more details in its proof. There are many other minor corrections, as well