标题： 通过分解映射的叶状结构分类 显示英文标题

标题： Classification of foliations via disintegration maps

摘要： 在本文中，我们提出了一种新方法，通过分解映射分析条件测度的支持与其在Wasserstein空间中的几何排列之间的关系。 我们的方法建立了确定此类条件测度何时来自度量测度叶状结构的准则。 此外，我们提供了一个具体示例，说明如何应用此框架来研究由分解诱导的叶状结构的变形（或扰动）。 显示英文摘要

摘要： 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.