Determination of the type and properties of the mapping function for certain classes of Riemann surfaces

[摘要] The purpose of this paper is to study three classes of surfaces, two classes consisting of simply connected surfaces and one class consisting of doubly connected surfaces. The singularities of the members of the classes will be classified using the classification of Iversen. If w = o is an isolated transcendental singularity of the Riemann surface F let Fo be the connected piece of F lying over |w - o| < r abutting on the singularity. Select r small enough so that no other transcendental singularity of F lies in Fo. Fo is mapped onto a domain Delta in the z-plane by a function z = ϕDelta (w) which consists of one or more uniform branches. The singularity is classified according to the behavior of the branches of ϕDelta (w) at w = o.

[发布机构] Rice University