Speaker: 潘会平教授，华南理工大学

Inviter: 刘劲松

Title: Ray structures on Teichmüller space

Language: Chinese

Time & Venue: 2026.07.03 09:00-10:00 南楼N913

Abstract: Given an oriented closed surface S of genus at least two, the Teichmüller space of S is the space of equivalence classes of complex structures on S. It is also the space of equivalence classes of hyperbolic structures on S. Deformations of these structures provide several types of ray structures on the Teichmüller space. In this talk, we will show a transition between Teichmüller geodesics and Thurston geodesics via harmonic map (dual) rays. As an application, we construct a new family of Thurston geodesics, the harmonic stretch lines, and show the existence and uniqueness of such lines for any two hyperbolic surfaces in the Teichmüller space. The key of the proof is a generalized Jenkins-Serrin problem: existence and uniqueness of some tree-valued minimal graphs over hyperbolic domains. This is a joint work with Michael Wolf.