有界单连通区域上解析逆紧映射的拓扑度

Topological Degree of Proper Holomorphic Mapping on Bounded Simply Connected Domains

设Ω和G都是边界局部连通的有界单连通区域,假设f是Ω到G的解析逆紧映射.通过将单连通区域提升至单位圆盘,本文得到了G的边界点的分支数和其逆象点分支数之间的等式关系,并讨论了f的拓扑度和逆象点个数之间的不等式关系.

Letting Ω and G be two simply connected domains with locally connected boundary, letting f be a proper holomorphic mapping from Ω onto G, and lifting Ω and G onto unit discs, in this work, we have obtained the equality relationship between component numbers of the point on dG and those of its different inverse image points on dG. The inequality relationship between the topological degree of f and the number of the different inverse image points is also obtained and discussed.