在青年基金资助下，王鹏和Dorfmeister，Brander等人合作，完成了一系列关于Willmore曲面的loop群研究。本课题期望在此基础上，利用可积系统中的Loop群方法刻画Willmore曲面的几何和分析性质，并讨论Willmore曲面的分类问题，包括Willmore曲面的奇点分类，Willmore球面、S^4中Willmore实射影平面、S^5中equivariant Willmore曲面(包括球面，圆柱面和环面)分类和广义equivariant Willmore曲面刻画，并在此基础上研究它们的Willmore泛函值分布问题，以及特殊Willmore环面的稳定性问题。

Under the support of NSFC for young researchers, Peng Wang, cooperated with Brander, Dorfmeister, finished a series of works on Willlmore surfaces via loop groups. Based on these works, we aim to provide more geometric and analytic descriptions and classifications of Willmore surfaces via loop groups. The main contents of this program contain the classification of singularities of Willmore surfaces, the classifications of Willmore two-spheres in S^n, Willmore RP^2 in S^4, equivariant Willmore surfaces in S^5 (including spheres, cylinders and tori), and generalized equivariant Willmore surfaces. Moreover, we also want to have a knowledge on the value distribution of the Willmore functional of these Willmore surfaces as well as the stability of Willmore tori with S^1 symmetry.