Excess函数的应用(英文)  

The Applications of Excess Function

作　　者：徐森林[1] 邓勤涛[1] 

机构地区：[1]华中师范大学数学与统计学学院,湖北武汉430079

出　　处：《应用数学》2007年第1期1-5,共5页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(10371047)

摘　　要：在本文中,我们研究了曲率有下界的开流形的拓扑,并推广了文[7]中的结果,证明了截曲率有下界的开流形如果它的excess函数被它的临界半径的某个函数所界定时,它就具有有限拓扑型或者微分同胚于Rn.In this paper,we study the topology of open manifolds with curvature bounded from below. We generalized the results in [7] and prove that an open manifold with sectional curvature bounded from below has finite topological type or is diffeomorphic to R^n when its excess is bounded by some function of its critical radius.

关 键 词：Excess函数 有限拓扑型 临界点 比较定理 

分 类 号：O186.16[理学—数学]