On the rigidity theorem for harmonic functions in Khler metric of Bergman type

作     者：LI Song-Ying 1,2, & WEI DongHuan 1 1 School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China 2 Department of Mathematics, University of California, Irvine, CA 92697-3875, USA 

作者机构：1. School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China2. Department of Mathematics University of California Irvine CA 92697-3875 USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2010年第53卷第3期

页      面：779-790页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by Minjiang Scholar Fund from FNU 

主　　题：rigidity pluriharmonic Laplace-Beltrami operators u-harmonic 

摘      要：The paper gives a method to generate the potential functions which can induce Khler metrics u = uij dz idz j of Bergman type on the unit ball B n in C n . The paper proves that if h ∈ C n (B n ) is harmonic in these metrics u ( u h = 0) in B n , then h must be pluriharmonic in B n . In fact, it is a characterization theorem, as a consequence, the paper provides a way to construct many counter examples for the potential functions of the metric u so that the above theorem fails. The results in this paper generalize the theorems of Graham (1983) and examples constructed by Graham and Lee (1988).