Speaker: Youliang Zhong（South China University of Technology）
Time: 10:30-11:30, Jul 19, 2025
Room: room 5103, the Fifth Teaching Building
While the Teichmüller space of hyperbolic conic surfaces provides a natural generalization of the classical theory, its fundamental geometric properties, including its deformation theory and metric structures, remain an active area of investigation.
First, we introduce a generalization of Thurston's earthquake to hyperbolic conic surfaces. A novel feature of our construction is that these deformations can change the cone angles. For the foundational case of a sphere with three conic points, we establish an analogue of the earthquake theorem, proving the existence of such maps while demonstrating the failure of uniqueness.
Second, motivated by understanding the metric geometry of these spaces, we study their length-spectrum metrics. We establish a uniform comparison between the metric defined by the length spectrum of simple closed curves and the metric defined by the length spectrum of simple arcs. This comparison holds for the subset of the Teichmüller space where all cone angles are not greater than $\pi$. This talk is based on joint works in progress with Yiyang Wu and Tianhui Chen, respectively.
