平均曲率流孤立子在平均曲率流的奇点分析中起到至关重要的作用。 在二维的情形，Ilmanen的猜想预测了可能出现的收缩孤立子的种类。本项目将以Ilmanen的猜想为指导， 结合近年来平均曲率流的发展， 尝试对二维平均曲率流收缩孤立子进行分类， 并以此为基础，进一步研究高维收缩孤立子和平移孤立子的几何结构。

The solitons play important roles in the study of singularity formations of the mean curvature flow. In the 2-dimensional case, the conjecture of Ilmanen predicts the rough classification of all the shrinking solitons. In this project, we shall follow the guidance of Ilmanen's conjecture and exploit the recent advances in the mean curvature flow study, to classify the mean curvature flow shrinking solitons. Furthermore, we shall study the geometric structure of high dimensional mean curvature flow shrinking and translating solitons.