带边流形上向量场的奇点指标公式及其应用  

An Index Formula of Singularities of Vector Fields on Manifolds with Boundary and Its Application

作　　者：徐栩[1] 

机构地区：[1]武汉大学数学科学学院,湖北武汉430072

出　　处：《武汉大学学报（自然科学版）》2001年第1期9-12,共4页Journal of Wuhan University(Natural Science Edition)

基　　金：国家自然科学基金!资助项目 (1 9971 0 81 )

摘　　要：讨论了M .Morse关于带边流形上向量场的奇点指标公式 ,应用延拓形变成adapted场的方法 ,给出了该公式一个更为简洁本质的证明 ,得到Rn 中单连通区域上连续映射的孤立零点估计 .它可以被看成是辐角原理的一般推广 .An index formula of singularities of vector fields on manifolds with boundary due to M.Morse was discussed. By using the method of deformation and extended to adapted fields, we get a more precise and essential proof of this index formula.As an appliction of it, an estimate of isolated zeros of continuous mapping on simply connected domain is obtained. It can be considered as a generalized version of the classical arguement principle.

关 键 词：带边流型 向量场 奇点指标公式 adapted场 孤立零点估计 辐角原理 延拓 

分 类 号：O189.3[理学—数学]