37000gcom威尼斯 2024 第12期 数理大讲堂

主讲人： 万学远 教授（重庆理工大学）

主持人： 冯惠涛 教授（南开大学）

讲座时间：2024年4月10日下午15:30-16:20

讲座地点：阿外楼酒店报告厅

讲座题目：Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space

摘要：In odd dimensions, we prove a scalar curvature rigidity for parabolic convex polytopes in hyperbolic space enclosed by linear planes in the Poincaré upper half-space model and convex with respect to the conformally related flat metric. Our method is based on spinor techniques and relies on the recent smoothing constructions of Brendle-Wang. We also prove a Llarull type rigidity for bounded smooth parabolic convex domains and a dihedral rigidity for polytopal initial data sets with dominant energy conditions. This work is joint with Xiaoxiang Chai.