Speaker: Wang Changliang, Distinguished Research Fellow, Tongji University

Date: November 7, 2025

Time: 14:30-15:30 pm

Location: B1032, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

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 closely related to the positive mass theorem. The studies of weak notions of positive scalar curvature motivate 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 recent 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.

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https://view.sdu.edu.cn/info/1020/207507.htm