小Excess与开流形的拓扑(英文)  

Small Excess and the Topology of Open Manifolds

作　　者：徐森林[1] 王作勤[1] 杨芳云[1] 

机构地区：[1]中国科学技术大学数学系,安徽合肥230026

出　　处：《应用数学》2002年第4期7-12,共6页Mathematica Applicata

基　　金：ProjectSupportedbyNNSFC( 199710 81)

摘　　要：本文中 ,我们应用比较几何的方法研究开流形的Excess与其拓扑之间的关系 .我们证明了对于一个曲率下有界的开流形 ,当它的Excess被其临界半径的某个函数所界定时 ,它就有有限拓扑型或微分同胚于n维z欧氏空间 .In this paper, we study the relations between the excess of open manifolds and their topology by using the methods of comparison geometry. We prove that for an open manifold with curvature bounded from below, it has finite topological type or it is diffeomorphic to R ~n when its excess is bounded by some function of its critical radius.

关 键 词：Excess函数 开流形 有限拓扑型 临界点 比较定理 

分 类 号：O186.16[理学—数学]