论文标题
奇异双曲线指标和负谐波功能
Singular hyperbolic metrics and negative subharmonic functions
论文作者
论文摘要
我们提出了一个猜想，即在$ {\ rm psl}中{\ it zariski struction {\ rm psl}（2，\，\，{\ bbb r}）中的单数双曲度度量的单型组是{\ it zariski strice}）$。通过使用Meromormorphic差异和仿射连接，我们获得了一个猜想的证据，即单数双曲度度量的单型组不能包含在四类的$ {\ rm psl}的一维谎言亚组中（2，\，\，\，{\ bbb r}）$。此外，我们确认了猜想，如果riemann表面是曾经被刺穿的Riemann Sphere之一，两次刺穿的Riemann Sphere，一个曾经刺穿的圆环和紧凑的Riemann表面。
We propose a conjecture that the monodromy group of a singular hyperbolic metric on a non-hyperbolic Riemann surface is {\it Zariski dense} in ${\rm PSL}(2,\,{\Bbb R})$. By using meromorphic differentials and affine connections, we obtain an evidence of the conjecture that the monodromy group of the singular hyperbolic metric can not be contained in four classes of one-dimensional Lie subgroups of ${\rm PSL}(2,\,{\Bbb R})$. Moreover, we confirm the conjecture if the Riemann surface is either one of the once punctured Riemann sphere, the twice punctured Riemann sphere, a once punctured torus and a compact Riemann surface.
