Speaker: Qiyu Chen（South China University of Technology）
Time: 09:00-10:00, Jul 19, 2025
Room: room 5103, the Fifth Teaching Building
We are interested in the parametrizations and deformations of hyperbolic cone-surfaces with variable positive cone angles. Based on the triangulations of surfaces instead of pants decompositions, we construct local coordinates of the Teichmüller space, including the circular foliation coordinates and the shear-radius coordinates (which can be viewed as the extension to hyperbolic cone-surfaces of the horocyclic foliations and shear coordinates established by Thurston). To achieve this, we introduce the space of measured foliation classes which are trivial around marked points and investigate its parametrizations. As applications, we define generalized stretch deformations and describe the asymptotic behaviors of two types of partial stretch rays. This is a joint work with Youliang Zhong.
