On singular metrics with
nonnegative scalar curvature and RCD
报告专家：王常亮 特聘研究员 （同济大学）
报告时间：6月26日（周五）10:00-11:00
报告地点：国家天元数学西南中心516
报告摘要：
The existence problem of smooth Riemannian metrics with positive scalar curvature has been well studied and many important results have been established, for example, its relation with the Yamabe constant, and resolution of Geroch conjecture, which is closed related to the positive mass theorem. The studies of weak notions of positive scalar curvature motivate to the studies of these problems for singular metrics. In this talk, I will review some previous results and report our works on this topic. In a joint work with Prof. Xianzhe Dai, Prof. Lihe Wang and Prof. Guofang Wei, we obtain a Geroch type result for uniformly Euclidean metrics, including a smooth extension result for uniformly Euclidean metric with nonnegative scalar curvature. This partially confirms a Schoen's conjecture for isolated singularity on spaces which are connected sums with torus. The theory of RCD space plays an important role in this work.
邀请人：盛利
