多复变数几何函数论

H.Cartan was the first mathematician to extend geometric function theory from one variable to several variables. Many works has been done after that, but the results were not systematical and.understanding, for the methods was too old. Since 1988, many mathematicians and I have worked deeply on this field by using several complex variables, differential geometry, Lie group, Lie algebra, etc, so that this branch to become lively. From then on, I have published two books in Chinese, forty articles, and my work is mainly about: 1.convex mappings of several complex variables；2.starlike mappings of several complex variables ； 3.Bloch constants of several complex variables ； 4.Schwarz derivatives of several complex variables；5.the representation.of Bergman kernel functions. All of these have made great influence in the world. Then, I have finished one book in Chinese and eleven articles in these three years. These works have made me to obtain the first class prize of Natural and Science of Chinese Academy Sciences in 2000, the lifetime achievement awards of Chinese Mathematical Society in 2002 and.the mathematical prize of Hua Loo-keng.

1933年H.Cartan开始研究如何将单复变数几何函数论推广到多复变数。几十年来有不少数学家进行研究，但进展不大。究其原因为所用工具落后。1988年以来我带领国内外一批数学家继承与发扬华罗庚学派传统及应用微分几何与李代数等近代数学理论，得到一系列深入的结果，使这个沉寂的方向重新活跃起来。我们现在处于国际领先地位，应继续保持之。