Mathematical Sciences: Nielsen Extensions and Kernels of Riemann Surfaces

该项目的目的是完善几个不等式，并延长有关有限黎曼曲面的尼尔森扩展的一些定理，并获得在尼尔森扩展过程中保持不变的曲面的模量。 这些结果将有助于更好地理解曲面与其Nielsen扩张之间的关系以及黎曼曲面上共形结构的分类。 使用数学软件，如Mathematica和Geomview的数值方法将用于调查的问题，通过获得数值和图形近似的共形函数映射到上半平面的尼尔森凸区域。

The purpose of the project is to refine several inequalities and to extend some theorems pertaining to Nielsen extensions of finite Riemann surfaces and to obtain moduli for surfaces which remain constant in the Nielsen extension process. These results would lead to a better understanding of the relationship between a surface and its Nielsen extension and the classification of conformal structures on Riemann surfaces. Numerical methods using mathematical software such as Mathematica and Geomview will be utilized in investigating the problems by obtaining numerical and graphical approximations of a conformal function mapping a Nielsen convex region onto the upper half-plane.