Singularity analysis for manifolds with Ricci curvature bounds

本项目旨在通过分析流形的拓扑结构和几何结构来研究流形奇点分析的中心问题。了解流形的几何结构是几何和拓扑学研究的前沿，在物理和医学成像等学科中也有应用。本项目将在这一活跃而充满活力的领域进行紧迫的研究，期望对极限空间有更深入的认识，深化几何测度理论，并加强其在数学和科学中的应用。

This project aims to investigate the central problem of singularity analysis in manifolds by profiling their topological structures and analysing their geometric structure. Understanding the geometric structure of manifolds is at the forefront of research in geometry and topology, with applications in disciplines such as physics and medical imaging. The project will undertake pressing research in this active and dynamic field and expects to generate greater understanding of limit spaces, deepening the theory of geometric measure theory, and enhancing their applications in mathematics and science.