Classification of foliations via disintegration maps

Florentin Münch, Renata Possobon, Christian S. Rodrigues

Published: 2025/9/17

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 concrete example demonstrating how this framework can be applied to study deformations (or perturbations) of disintegration-induced foliations.