关于可测叶状结构空间上两种线性结构的刚性

Rigidity about two linear structures on the space of measured laminations

通过黎曼曲面的双曲长度函数与极值长度函数,将可测叶状结构空间实现为Teichmüller空间的余切空间,从而诱导了可测叶状结构空间上的两种线性结构。证明了这两种线性结构都具有刚性性质,也即不同的黎曼曲面诱导不同的线性结构。

By modeling the space of projective measured laminations in the cotangent space to Teichmüller space via hyperbolic length functions and extremal length functions,we associate two classes of linear structures to the space of measured laminations.We prove that both of these two linear structures are rigid:the induced linear structures on different Riemann surfaces are different.