Research on constant mean curvature surfaces

1.我们将这些具有常高斯曲率的实二维黎曼流形的等长最小浸没归为一个复二维复空间形式。在本研究中，重要的是要证明这些浸入的Kaehler角的恒常性。我们研究了三维欧几里德空间中的周期旋转曲面，以理解常平均曲率曲面的重要性，并得到了周期函数为周期旋转曲面平均曲率的判据。此外，我们还发现了周期平均曲率函数与贝塞尔曲线之间的有趣关系。由于非零常平均曲率曲面的理论在这二十年中得到了很好的发展，我写了一本关于这一主题的教科书，以便对这一理论作一个统一的解释。最近，这本书被美国数学学会译成了英文。

1.We classified these isometric minimal immersions of real two dimensional Riemannian manifold with constant Gaussian curvature into a complex two dimensional complex space form. In this research, it was important to prove the constancy of the Kaehler angles of these immersions.2.We studied periodic surfaces of revolution in the three dimensional Euclidean space in order to understand the importance of constant mean curvature surfaces and got the criterion for a periodic function to be the mean curvature of a periodic surface of revolution. Moreover, we found an interesting relation between periodic mean curvature function and Bezier curves.3.Since the theory of non zero constant mean curvature surfaces is well developed on these twenty years, I have written a textbook about this subject in order to make a unified explanation of the theory. Recently, this book was translated into English by American Mathematical Society.