本项目主要对Alexandrov几何展开研究。基于多年的研究，我们发现在一个Alexandrov空间上某些距离函数达到最小值时会带来很多非常重要的几何信息，而且这可以衍生一种去寻找几何性质的方法，并非常值得研究。这个项目旨在利用这种方法在一个Alexandrov空间上去定义和寻找重要的子集，比如拟凸子集；寻找更为简单的方法刻画这种空间上的曲率；刻画某些具体的几何结构，尤其是Alexandrov空间中Join的模空间结构，以及相关的基本问题，比如Soul猜想。这些研究内容对Alexandrov几何而言，都是非常基础而且本质的，而且我们的方法和观点都具有很好的创新性。我们相信这个项目的研究会对Alexandrov几何有着基础性的贡献，而且我们相信这个项目的可行性非常大。

This research project focuses mainly on Alexandrov geometry. Based on years of work experience, we observe that some important geometries can be seen when distance functions attain minimums in an Alexandrov space, and from this an approach can be derived to look for beautiful geometries, which is very worthy of research and study. This project aims to apply such an approach to define and study important subsets in an Alexandrov space, for instance, quasi-convex subsets; to look for a much easier viewpoint to illustrate the curvature of Alexandrov spaces; to study some concrete geometric structure, especially the structure of module spaces of Joins in Alexandrov spaces, and some related problems, for instance, Soul conjecture. These research contents are all fundamental and essential to Alexandrov geometry, and almost all of our research methods are new and original.