Studies on compactifications of Teichmuller spaces

除了与黎曼球面共形的黎曼曲面减去圆盘和一点或两点外，本文证明了拓扑有限型黎曼曲面的Teichmuller空间可以通过适当选择简单闭测地线的长度函数实现为有限维真实的射影空间中的多面体。还考虑了Teichmuller空间的Thurston边界。明确地构造了环面上退化的黎曼曲面族，并确定了它们的奇异纤维和全纯截面。

Except Riemann surfaces conformal to Riemann spheres minus disks and one or two points, I showed that Teichmuller spaces of RIemann surfaces of topologically finite types can be realized as polyhedron in finite dimensional real projective spaces by means of length functions of suitable choices of simple closed geodesics. Thurston boundaries of Teichmuller spaces were also considered. I also constructed degenerate families of Riemann surfaces over tori explicitly, and determined their singular fibers and holomorphic sections.