非塌缩Ricci极限空间的分析

由于Ricci极限空间理论在解决凯勒爱因斯坦度量的存在性问题、解决Hamilton-田刚猜想以及研究流形基本群的结构中起到非常重要作用，并且它的研究与很多方向都有着密切的联系，使得研究Ricci极限空间理论非常活跃。本项目主要目的是深入拓展该理论，研究非塌缩Ricci曲率有下界流形的极限空间。 我们将研究极限空间的拓扑奇点与正则点的bilipschitz结构问题：.（1） 研究极限空间局部拓扑非欧氏的奇点。.（2） 研究极限空间正则点的bilipschitz结构。..这方面的研究将会极大地提升人们对Ricci曲率的理解，并且对研究调和映照、极小曲面、Yang-Mills场等相关领域有很大帮助。

The study of Ricci limit spaces has closed relations with many areas. Moreover, due to the powerful applications of the study of Ricci limit space to the resolution of the existence of Kahler-Einstein metric, the resolution of Hamilton-Tian conjecture and the study of fundamental groups, it is very active to study Ricci limit spaces. The main aim of this proposal is to extend such theory by studying the Gromov-Hausdorff limits of noncollapsing manifolds with uniform lower Ricci curvature bounds. We will concern the topological singular and the bilipschitz structure of regular points of limit spaces:.(1) Study the non-Euclidean topological singular set..(2) Study the bilipschitz structure of regular set...This study will greatly improve our understanding of Ricci curvature. Furthermore the study will be applied to the study of harmonic maps、 minimal surfaces、Yang-Mills fields and related areas.