Year: 2018
Type: article
Abstract: We describe the effect of Fenchel-Nielsen coordinates under elementary move for hyperbolic surfaces with geodesic boundaries, punctures and cone points, which generalize Okai's result for surfaces with geodesic boundaries. The proof relies on the parametrization of the Teichmüller space of surface of type (1,1) or (0,4) as a sub-locus of an algebraic equation in $\mathbf{R}^3$. As an application, we show that the hyperbolic length functions of closed curves are asymptotically piecewise linear functions with respect to the Fenchel Nielsen coordinates in the Teichmüller spaces of surfaces with cone points.
Source: Kodai Mathematical Journal
Authors: Dong Tan, Peijia Liu, Xuewen Liu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G2019863827, G4954962329
OpenAlex ID: W2809986115