勷勤数学•专家报告

题      目：Ray structures on Teichmüller space

报  告  人： 潘会平 教授  (邀请人：黄志波)

                                   华南理工大学

时      间： 7月6日  15：30-16:30

地     点：数科院东楼401

报告人简介:

       潘会平，华南理工大学数学学院教授，研究方向为复分析（Teichmüller 理论）,主要研究曲面上的复结构、双曲结构、平坦结构等几何结构，以及这些结构之间的形变，相关论文在Acta Math.、 Math. Ann.、Trans. Amer. Math. Soc.、Int. Math. Res. Not. IMRN、Sci. China Math.等期刊发表或接受发表。

摘      要：

       Given an oriented closed surface S of genus at least two, the Teichmuller 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 Teichmuller space. In this talk, we will show a transition between Teichmuller 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 Teichmuller 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.

          欢迎老师、同学们参加、交流！