万有Teichmüller空间不同模型中的测地线唯一性

Uniqueness of geodesics in different models of universal teichuller space

研究万有Teichmülle空间不同模型中的测地线的唯一性问题。证明了在万有Teichmülle空间中存在两个点,它们之间的测地线唯一,但在万有Teichmülle空间的Schwarz导数与Pre-Schwarz导数模型中,这两个点所对应的点之间的测地线不唯一。

The uniqueness problem of geodesics in different models of the universal Teichmuller space was studied.It proved thaatt there is a unique geodesic segment joining two points in the universal Teichmuller space.However,in the Schwarzian derivative and Pre-Schwarzian derivative models,there are more than one geodesic segment joning the corresponding points in the universal Teichmuller space