Hadamard流形中子流形的p-调和函数的刘维尔型定理  

Liouville Type Theorems for p-harmonic Functions on Submanifolds in a Hadamard Manifold

作　　者：韩英波 蒋凯歌 张倩玉 HAN Yingbo;JIANG Kaige;ZHANG Qianyu(College of Mathematics and Statistics,Xinyang Nornal University,Xinyang 464000,China;School of Mathenatics,Sun Yat-Sen University,Guangzhou 510275,China;College of Electromechanical and Information Engineering,Chongqing College of Humanities,Science and Technology,Chongqing 401524,China)

机构地区：[1]信阳师范学院数学与统计学院,河南信阳464000 [2]中山大学数学学院,广东广州510275 [3]重庆人文科技学院机电与信息科学学院,重庆401524

出　　处：《信阳师范学院学报（自然科学版）》2019年第1期11-16,共6页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11201400);信阳师范学院南湖学者"青年项目"(A类);河南省高校骨干教师培养计划项目(2016GGJS-096)

摘　　要：若Hadamard流形中的完备非紧可定向子流形具有有限全曲率且截面曲率非正,证明了当光滑函数u的Lp范数有限时,任何的p-调和函数一定是一个常数(p≥2).Let m-dinensional complete non-compact oriented submanifolds in Hadamard manifolds have finite total curvature and non-positive sectional curvature. Further, it is assumed that the first eigenvalue of Laplacian in M is bounded by an appropriate constant. Then,when the norm of L^p of the smooth function w is finite,any p-hannonic function must be a constant(p≥2).

关 键 词：p-调和函数 刘维尔型定理 子流形 

分 类 号：O186.1[理学—数学]