有界星形圆型域上的零伦全纯映照  

Null-Homotopic Holomorphic Mappings on the Bounded Starlike Circular Domains

作　　者：刘爱超[1] 崔艳艳[2] 刘浩[3] 

机构地区：[1]黄淮学院数学科学系,河南驻马店463000 [2]周口师范学院数学与信息科学系,河南周口466000 [3]河南大学数学与信息科学学院,河南开封475004

出　　处：《数学的实践与认识》2013年第17期247-254,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11271359);河南省计划项目(112300410251)

摘　　要：星形映照与螺形映照是多复变函数论中两个重要的映照类,他们共同的几何特征是其像域中任一点到原点的直线或螺线完全落在该像域中.利用拓扑学知识,从同伦的观点出发研究具有上述几何特征的映照,并得出其上的零伦全纯映照的判别方法,所得结论对复欧式空间C^n中的单位球B^n同样成立.Starlike mappings and spirallike mappings are two ofthe most important mappings in geometric theory of several complex variables. Their same geometric characterization is that the closed line segment or spiral joining each point in their image domains to zero lies entirely in their image domains. According to topology knowledge, westudy mappings with above geometric features, and draw distinguishing method of null-homotopic holomorphic mappings from the point of view of the homotopy.Zhese results are true for the unit ball in complex Euclidean space.

关 键 词：星形映照 螺形映照 零伦全纯映照 有界星形圆型域 

分 类 号：O174.52[理学—数学]