非负曲率流形上的调和函数空间  

SPACES OF HARMONIC FUNCTIONS ON COMPLETE MANIFOLDSWITH NON-NEGATIVE CURVATURE

作　　者：邓严林[1] 李光汉[2] 李成银 

机构地区：[1]沙洋师范高等专科学校数学系,湖北荆门448200 [2]湖北大学数学与计算机学院,湖北武汉430062

出　　处：《荆州师范学院学报》2002年第5期8-10,58,共4页Journal of Jingzhou Teachers College

摘　　要：设Ω(M )表示在M的每个端上至少一边有界的调和函数空间 ,当M完备非紧且其截曲率在一紧致集外非负时 ,维数为M的大端和小端的个数之和 ;当M的Ricci曲率处处非负时 ,维数的上界为 3,若此时M含有三个抛物端 ,则Ω(M )的维数等于Let Ω(M) be the linear space spanned by the set of harmonic functions on M which are bounded on one side at each end .When M is a complete non-compact manifold without boundary and the sectional curvature of M is non-negative outside a compact subset of M ,we show that the dimension of space is the numbers of large and small ends of M .When M is non-negatively Ricci curved every where ,we show that the upper bound of dimension is 3.Moreover, if M only consists of 3 parabolic ends,dim Ω(M) is 3.

关 键 词：非负曲率流形 调和函数空间 端 完备非紧流形 截曲率 RICCI曲率 

分 类 号：O186.16[理学—数学]