Abstract: Llarull's Theorem states that on an n-sphere, a Riemannian metric dominating the standard one must have scalar curvature less than n(n-1) at some point. Utilizing Llarull's proof, we have obtained a stability result in the intrinsic flat sense, assuming a uniformly bounded Poincaré constant. Additionally, I will share the proof of the Incomplete Llarull's Theorem for dimension three, using level set techniques. These works are joint efforts with Sven Hirsch, Demetre Kazaras, and Marcus Khuri.  

Bio-Sketch: Yiyue Zhang is a visiting assistant professor at UCI, working with Prof. Richard Schoen. His primary research interests include scalar curvature and interconnected topics such as level set methods, minimal surfaces, and spin geometry, along with their applications in general relativity. He earned his PhD degree from Duke University under the supervision of Prof. Hubert Bray in 2021.

Zoom: https://us02web.zoom.us/j/83960986853?pwd=NHhFdXU5WnVTcWFyVzFzSmtJSCtWUT09                                                                          Meeting ID: 839 6098 6853    Passcode: 104348