Xianzhe Dai
University of California Santa Barbara
Title
Singular metrics of nonnegative scalar curvature and RCD
Abstract
The positive mass theorem of Schoen-Yau and Witten is one of the landmark results and it is closely related to the existence of positive scalar curvature metrics. Various motivations lead to consideration of singular metrics. I will first review these and present our work with Yukai Sun and Changliang Wang on positive mass theorem and Geroch type theorem for isolated conical singularity. Then I will discuss our very recent work on singular metrics with nonnegative scalar curvature with small singularity, in particular confirming Schoen's conjecture for isolated singularity on spaces which are connected sums with the torus. Crucial to our approach is the novel connection with RCD spaces, singular spaces having some weak Ricci curvature bound. This part of the work is joint with Changliang Wang, Lihe Wang, and Guofang Wei.
