Study on Riemann surfaces and Klein surfaces with hyperbolic regular polygons as their fundamental regions

我们解决了极值Klein曲面中嵌入了多少个极值圆盘的问题，并根据极值圆盘的数量、极值圆盘的位置和自同构群对这些曲面进行了分类。为此，我们使用双曲正多边形作为它们的基本区域。对于具有双曲正则多边形的亏格为2的Riemann曲面，通过基于Weerstrass点重构基本区域，给出了曲面的TeichMuller空间方程和齐次坐标方程。

We solved the problem that how many extremal discs are embedded in extremal Klein surfaces, and classified these surfaces by the number of extremal discs, location of extremal discs, and the group of automorphisms. For this aim we used hyperbolic regular polygons as their fundamental regions. As for Riemann surfaces of genus two with hyperbolic regular polygons we gave equations of the Teichmuller space and homogeneous coordinates for the surfaces by reconstructing fundamental regions based on the Weierstrass points.