报告题目：Rigidity of hyperbolic polyhedral 3-manifolds

报告人：葛化彬教授 (中国人民大学)

报告时间：2023年12月29日下午14:00-15:00

报告地点：数学楼112会议室

报告摘要：

We show the rigidity of hyperbolic polyhedral metrics on 3-manifolds. By definition, such manifolds are isometric gluing of decorated hyperbolic tetrahedra. Here a decorated hyperbolic tetrahedron is a hyperbolic tetrahedron with only ideal or hyper-ideal vertices, and furthermore, with a horosphere called decoration centered at each ideal vertex. We show that the above hyperbolic polyhedral metric is determined up to isometry and change of decorations by its curvature. This work generalized Luo-Yang's rigidity results [2018, J. Topol.] to the most general situation. This is joint work with Ke Feng and Chunlei Liu.

报告人简介：

葛化彬，中国人民大学数学学院教授，博士生导师。博士毕业于北京大学数学科学学院，曾获得国家优秀青年科学基金项目。主要研究方向为几何拓扑，推广了柯西刚性定理和Thurston圆堆积理论，部分解决Thurston的“几何理想剖分”猜想、完全解决Cheeger-tian、林芳华的Ricci曲率正则性猜想，相关论文分别发表在Geom. Topol., Geom. Funct. Anal., Amer. J. Math., Adv. Math.等权威数学期刊。