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

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.