报告学者：韩肖垄

报告者单位：上海数学与交叉学科研究院和复旦大学

报告时间：2025/03/10  1:00-2:00 pm

报告地点：七教7215

 

Abstract:         A surface S in a manifold M is filling if S cuts M into contractible components. We prove for any closed hyperbolic 3-manifold M , there exists a K”> 0 such that every homotopy class of K-quasi-Fuchsian surfaces with 1 ≤ K ” is filling. As a corollary, the set of embedded surfaces in M satisfies a dichotomy: it consists of at most finitely many totally geodesic surfaces and surfaces with a quasi-Fuchsian constant lower bound K ” .  Each of these nearly geodesic surfaces separates any pair of distinct points at the sphere of  infinity. Crucial tools include the rigidity results of  Mozes-Shah, Ratner, and Shah. This work is inspired by a question of  Yunhui Wu and Yuhao Xue whether random geodesics on random hyperbolic surfaces are filling.

 

报告学者简介：韩肖垄在美国伊利诺伊大学香槟分校获得博士学位，师从Nathan M. Dunfield教授，并在清华大学丘成桐数学科学中心由吴云辉教授指导完成博士后研究，目前在上海数学与交叉学科研究院与复旦大学担任讲师。研究领域为双曲几何和低维流形