Characterization of foliations via disintegration maps
arXiv:2509.14209 · doi:10.1007/s00526-026-03308-2
Abstract
In this paper, we present a novel approach for analyzing the relationship between the supports of conditional measures and their geometric arrangement in Wasserstein space via the disintegration map. Our method establishes criteria to determine when such conditional measures arise from a metric measure foliation. Additionally, we provide a example demonstrating how this framework can be applied to study perturbations of disintegration-induced foliations.
17 pages, 4 figures