Time：16:00-17:00, Friday, Sep 16, 2022
Venue: Room E4-233, Yungu Campus, Westlake University
Host: Dr. Xing Gu, Institute for Theoretical Sciences, Westlake University
Speaker：Dr. Jie Xu, Institute for Theoretical Sciences, Westlake University
Title：The Yamabe-type Problems on Various Domains
Abstract：The Yamabe problem is a high dimensional generalization of the uniformization theorem on Riemann surfaces, which concerns the existence of a Yamabe metric that admits a constant scalar curvature. In this talk, we review the proof of the Yamabe problems on closed manifolds, which has been done by Yamabe, Aubin, Trudinger, and Schoen. We then discuss new proofs of the Yamabe-type problems on small Riemannian domain, on closed manifolds, on compact manifolds with boundary, etc. In particular, we show how to use new methods other than global calculus of variations to completely solve the Escobar problem and the Han-Li conjecture.
